The Global Economy - NYU Stern

The Global Economy

The Global Economy

Version 2.2

NYU SternDepartment of Economics

This document was created for the Global Economy course at New YorkUniversity’s Stern School of Business by a team that includes Dave Backus,Gian Luca Clementi, Tom Cooley, Joe Foudy, Kim Ruhl, Kim Schoenholtz,Laura Veldkamp, Venky Venkateswaran, Paul Wachtel, Mike Waugh, andStan Zin. The cover was designed by Alexa Zin. The most recent version ofthis document, and related materials, will be posted at

https://github.com/DaveBackus/Amazon_Global_Economy.

This version was created August 24, 2015.

Copyright c© 2015 by New York University’s Center for Global Economyand Business

This work is licensed under the Creative CommonsAttribution-ShareAlike 3.0 Unported License.

To view a copy of this license, visithttp://creativecommons.org/licenses/by-sa/3.0/.

https://github.com/DaveBackus/Amazon_Global_Economy

http://creativecommons.org/licenses/by-sa/3.0/

Contents

Preface ix

I Preliminaries 1

1 Mathematics Review 3

1.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Exponents and logarithms . . . . . . . . . . . . . . . . . . . . . 41.3 Growth rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Slopes and derivatives . . . . . . . . . . . . . . . . . . . . . . . 101.5 Finding the maximum of a function . . . . . . . . . . . . . . . . 121.6 Spreadsheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.7 Getting data from FRED . . . . . . . . . . . . . . . . . . . . . 14

2 Macroeconomic Data 19

2.1 Measuring GDP . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2 Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3 Distinguishing prices from quantities . . . . . . . . . . . . . . . 262.4 Fine points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

II Long-Term Economic Performance 39

3 The Production Function 45

3.1 The production function . . . . . . . . . . . . . . . . . . . . . 453.2 Capital input . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3 Labor input . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.4 Productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.5 Marginal products . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 The Solow Model 57

4.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

v

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4.2 Capital dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 584.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.4 Impact of saving and investment . . . . . . . . . . . . . . . . . 634.5 Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5 Sources of Economic Growth 69

5.1 Cross-country differences in output per worker . . . . . . . . . . 695.2 Cross-country differences in growth rates . . . . . . . . . . . . . 715.3 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6 Institutions and Policies 79

6.1 Good institutions . . . . . . . . . . . . . . . . . . . . . . . . . 796.2 Institutions or policies? . . . . . . . . . . . . . . . . . . . . . . 81

7 Labor Markets 87

7.1 Indicators of labor-market “status” . . . . . . . . . . . . . . . . 887.2 Supply and demand for labor . . . . . . . . . . . . . . . . . . . 897.3 Supply and demand with a minimum wage . . . . . . . . . . . 917.4 Labor-market institutions . . . . . . . . . . . . . . . . . . . . . 937.5 Labor-market flow indicators . . . . . . . . . . . . . . . . . . . 937.6 Virtues of flexible input markets . . . . . . . . . . . . . . . . . 947.7 A model of unemployment dynamics . . . . . . . . . . . . . . . 967.8 Institutions and labor-market dynamics . . . . . . . . . . . . . . 98

8 Financial Markets 105

8.1 Features of effective financial markets . . . . . . . . . . . . . . 1058.2 Financial regulation and crises . . . . . . . . . . . . . . . . . . 106

9 International Trade 109

9.1 Ricardo’s theory of trade . . . . . . . . . . . . . . . . . . . . . 1109.2 Digging a little deeper . . . . . . . . . . . . . . . . . . . . . . . 1129.3 Wages and productivity . . . . . . . . . . . . . . . . . . . . . . 1169.4 Bottom line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1179.5 Winners and losers . . . . . . . . . . . . . . . . . . . . . . . . . 118

III Short-Term Economic Performance 121

10 Business-Cycle Properties 127

10.1 Cycles and volatility . . . . . . . . . . . . . . . . . . . . . . . 12810.2 Expenditure components . . . . . . . . . . . . . . . . . . . . . 12910.3 Labor and capital markets move with the cycle . . . . . . . . . 130

CONTENTS vii

11 Business-Cycle Indicators 135

11.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13611.2 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13611.3 Good indicators . . . . . . . . . . . . . . . . . . . . . . . . . . 13711.4 Identifying good indicators . . . . . . . . . . . . . . . . . . . . 13811.5 The business-cycle scorecard . . . . . . . . . . . . . . . . . . . 14211.6 Regression-based forecasting . . . . . . . . . . . . . . . . . . . 14511.7 Aggregation and prediction markets . . . . . . . . . . . . . . . 146

12 Money and Inflation 151

12.1 The quantity theory . . . . . . . . . . . . . . . . . . . . . . . 15212.2 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15312.3 Changing the money supply . . . . . . . . . . . . . . . . . . . . 15412.4 Big Inflations . . . . . . . . . . . . . . . . . . . . . . . . . . . 15612.5 Inflation and interest rates . . . . . . . . . . . . . . . . . . . . 15712.6 Velocity reconsidered . . . . . . . . . . . . . . . . . . . . . . . 159

13 Aggregate Supply and Demand 163

13.1 Aggregate supply . . . . . . . . . . . . . . . . . . . . . . . . . 16413.2 Aggregate demand . . . . . . . . . . . . . . . . . . . . . . . . 16613.3 Aggregate supply and demand together . . . . . . . . . . . . . 16713.4 Beyond supply and demand . . . . . . . . . . . . . . . . . . . . 170

14 Policy in the AS/AD model 175

14.1 Objectives of policy . . . . . . . . . . . . . . . . . . . . . . . . 17514.2 Policy responses to supply and demand shocks . . . . . . . . . . 176

15 Money and Interest Rates 185

15.1 Interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18615.2 Changing the money supply (review) . . . . . . . . . . . . . . . 18715.3 Managing the interest rate . . . . . . . . . . . . . . . . . . . . 18915.4 Goals of monetary policy . . . . . . . . . . . . . . . . . . . . . 19115.5 The Taylor rule: the bond trader’s guide . . . . . . . . . . . . 19315.6 Deflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19615.7 Quantitative easing, credit easing, and signaling . . . . . . . . . 196

IV Crises and Other Topics 201

16 Taxes 205

16.1 Social cost of taxes . . . . . . . . . . . . . . . . . . . . . . . . 20616.2 The benefits of a broad tax base . . . . . . . . . . . . . . . . . 20816.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

viii Global Economy @ NYU Stern

17 Government Debt and Deficits 219

17.1 Government revenues, expenses, and debt . . . . . . . . . . . . 22017.2 Debt and (primary) deficits . . . . . . . . . . . . . . . . . . . . 22017.3 Debt dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 22217.4 What’s missing? . . . . . . . . . . . . . . . . . . . . . . . . . . 22517.5 How much debt is too much? . . . . . . . . . . . . . . . . . . . 226

18 International Capital Flows 231

18.1 Trade in goods, services, and income . . . . . . . . . . . . . . . 23218.2 Trade in assets . . . . . . . . . . . . . . . . . . . . . . . . . . . 23318.3 Net foreign assets . . . . . . . . . . . . . . . . . . . . . . . . . 23418.4 Sources of external deficits . . . . . . . . . . . . . . . . . . . . 23518.5 Debt dynamics and sustainability . . . . . . . . . . . . . . . . 23618.6 Big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

19 Exchange-Rate Fluctuations 241

19.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24219.2 Properties of exchange rates . . . . . . . . . . . . . . . . . . . 24319.3 Purchasing-power parity . . . . . . . . . . . . . . . . . . . . . 24319.4 Depreciation and inflation . . . . . . . . . . . . . . . . . . . . . 24619.5 Interest rate parity and the carry trade . . . . . . . . . . . . . 24819.6 Predicting exchange rates . . . . . . . . . . . . . . . . . . . . . 250

20 Exchange-Rate Regimes 255

20.1 A catalog of foreign-exchange arrangements . . . . . . . . . . . 25520.2 Fixed exchange rates . . . . . . . . . . . . . . . . . . . . . . . 25620.3 Sterilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25820.4 The trilemma . . . . . . . . . . . . . . . . . . . . . . . . . . . 25820.5 Exchange-rate crises . . . . . . . . . . . . . . . . . . . . . . . . 25920.6 Strong fixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

21 Macroeconomic Crises 263

21.1 Classic crisis triggers . . . . . . . . . . . . . . . . . . . . . . . 26321.2 Crisis indicators: the checklist . . . . . . . . . . . . . . . . . . 26421.3 Crisis responses . . . . . . . . . . . . . . . . . . . . . . . . . . 266

Index 274

Preface

This document evolved from a set of notes developed for the Global Economycourse at New York University’s Stern School of Business. The idea behindthe course is to use the tools of macroeconomics to assess the economicperformance of countries and the challenges facing businesses operating inthem. We emphasize data; virtually every chapter includes links to datasources. The book is designed as background reading for the in-class expe-rience. The focus is on tools, leaving us to spend most of our class time onapplications.

We have posted all of our materials online and offer them to others with sim-ilar interests in the hope that they will reciprocate. “We” here means theGlobal Economy team: Dave Backus, Gian Luca Clementi, Tom Cooley, JoeFoudy, Kim Ruhl, Kim Schoenholtz, Laura Veldkamp, Venky Venkateswaran,Paul Wachtel, Mike Waugh, and Stan Zin. This set of notes is available on-line at

https://github.com/DaveBackus/Amazon_Global_Economy.

The same site includes all of the files used to produce the manuscript, in-cluding the Stata programs used to generate figures and tables. The onlineversion of the notes includes color graphs and an extensive collection of links.We offer an inexpensive black-and-white printed version through Amazon,self-published through their CreateSpace facility, which we were delightedwith.

We’re equally interested in your thoughts: on the course, the materials,teaching macroeconomics, or anything else that crosses your mind. Send usan email, we’re easy to track down.

One last request: Please pass on any typos or other glitches you find. Yourefforts will help us improve future versions.

ix

https://github.com/DaveBackus/Amazon_Global_Economy

x Global Economy @ NYU Stern

Part IPreliminaries

1

1Mathematics Review

Tools: Exponents and logarithms; growth rates and compounding; deriva-tives; spreadsheets; the FRED database.

Key Words: Production function; demand function; marginal product;marginal cost.

Big Ideas:

• Macroeconomics is a quantitative discipline; ditto business.

• Mathematics and data analysis are essential tools.

Mathematics is a precise and efficient language for expressing quantitativeideas, including many that come up in business. What follows is an executivesummary of everything you’ll need in this course: functions, exponents andlogarithms, derivatives, and spreadsheets, each illustrated with examples.

1.1 Functions

In economics and business, we often talk about relations between variables:Demand depends on price; cost depends on quantity produced; price de-pends on yield; output depends on input; and so on. We call these relationsfunctions. More formally, a function f assigns a (single) value y to eachpossible value of a variable x. We write it this way: y = f(x). Perhaps theeasiest way to think about a function is to draw it: Put x on the horizontalaxis and plot the values of y associated with each x on the vertical axis. Ina spreadsheet program, you might imagine setting up a table with a grid of

3

4 Global Economy @ NYU Stern

values for x. The function would then be a formula that computes a valuey for each value of x.

Example: Demand functions. We may be interested in the sensitivity ofdemand for our product to its price. If the quantity demanded is q and theprice p, an example of a demand function relating the two is

q = a+ bp,

where a and b are “parameters” (think of them as fixed numbers whosevalues we haven’t bothered to write down). Sensitivity of demand to priceis summarized by b, which we’d expect to be negative (demand falls as pricerises).

Example: Production functions. In this class, we’ll relate output Y toinputs of capital K and labor L. (In macroeconomics, capital refers to plantand equipment.) It’ll look a little strange the first time you see it, but aconvenient example of such a function is

Y = KαL1−α,

where α is a number between zero and one (typically, we set α = 1/3). Thisis a modest extension of our definition of a function—Y depends on twovariables, not one—but the idea is the same.

Example: Bond yields. The price p and yield y for a one-year zero-couponbond might be related by

p =100

1 + y,

where 100 is the face value of the bond. Note the characteristic inverserelation: high yield, low price.

1.2 Exponents and logarithms

Exponents and logarithms are useful in many situations: elasticities, com-pound interest, growth rates, and so on. Here’s a quick summary.

Exponents. Exponents are an extension of multiplication. If we multiplyx by itself, we can write either x × x or x2, where 2 is an exponent (orpower). In general, we can write xa to mean (roughly) “x multiplied byitself a times,” although this language may seem a little strange if a isn’t apositive whole number such as 2 or 3. We can, nevertheless, compute suchquantities for any value of a we like as long as x is positive. (Think abouthow you’d do this in a spreadsheet.)

1. Mathematics Review 5

The most useful properties of exponents are

xaxb = xa+b

xaya = (xy)a

(xa)b = xab

x−a = 1/xa.

You can work these out for yourself using our multiplication analogy.

Logarithms. By logarithm, we mean the function “LN” in Microsoft Ex-cel, OpenOffice Calc, or Google spreadsheets, sometimes called the naturallogarithm.

The natural logarithm of a number x comes from the power of a number e,a mathematical constant that is approximately 2.718. If x = ey, then y isthe logarithm of x, expressed y = lnx. There are other logarithms basedon powers of other numbers, but we’ll stick with e. Some people use logto mean ln, but that’s a story for another time. In this class, includingassignments and exams, we always use ln and LN, not log or LOG.

Suppose that you know that y is the logarithm of x. How do you find x?From the definition, apparently x = ey. In Excel, this is written “exp(y).”As a check, you might verify that ln 6 = 1.792 and exp(1.792) = 6.00.

The most useful properties of logarithms are:

ln(xy) = lnx+ ln y

ln(x/y) = lnx− ln y

ln(xa) = a lnx

ln(exp(x)) = x

exp(lnx) = x

ln(1 + x) ≈ x, when x is small.

The wiggly equals sign means “approximately equal to.” That’s true for thelast equation when x is close enough to zero: a number like 0.1 rather than0.9 or 1.2 or 10. In short, logarithms convert multiplication into addition,division into subtraction, and “exponentiation” into multiplication. In eachcase, an operation is converted into a simpler one: Addition, for example, issimpler than multiplication.

Example: Demand functions. A more useful demand function is q = apb,which is linear in logarithms:

ln q = ln a+ b ln p.


This follows from the first and third properties of logarithms. Here, b is theprice elasticity you may have learned about in a microeconomics class.

Example: Production functions. Understanding differences in output perworker (across production units, firms, countries) is a central question inmacroeconomics and this course. Using the production function discussedabove, we can use properties of exponents to arrive at an expression suitablefor this analysis. Using the production function

Y = KαL1−α,

use the first and last property of exponents to obtain

Y = KαLL−α

= KαL(1/Lα).

Combining the terms with the α exponent and then using the second prop-erty of exponents, we have

Y = (K/L)αL.

Finally, dividing both sides by L leaves us with the expression

Y/L = (K/L)α.

In words, output per worker equals capital per worker to the exponent α.

1.3 Growth rates

Growth rates are frequently used in this class, in the business world, andin life in general. We will use two types — sorry, it can’t be avoided. Thefirst is a discretely-compounded growth rate. For a time interval of one year,this is analogous to an annually-compounded interest rate. The second is acontinuously-compounded growth rate. This is analogous to a continuously-compounded interest rate, in which interest is compounded over a very shorttime interval. The former is more natural is some respects, but the latterleads to simpler expressions when compounding is important.

Discretely-compounded growth rates

The simplest growth rates are those that are compounded each period t atdiscrete time intervals. If the time period is a year (which will frequently bethe case), then this corresponds with annual compounding. The annuallycompounded growth rate relates variable x across time periods as

xt+1 = (1 + g)xt,


where lower case g will denote the discretely-compounded growth rate.

Notation note: We will always denote the discretely-compounded growthrate as g.

To compute this growth rate from data on x, one can use the formula

g = (xt+1/xt)− 1 = (xt+1 − xt)/xt.

If we want to express this growth rate as a percent, we multiply it by 100.

Example: The FRED database reports that annual US real Gross DomesticProduct (GDP) (measured in 2009 dollars) in 2010 was 14,779.4 billion.For 2011, annual US real GDP was 15,052.4 billion. The annual (discretecompounded) growth rate of US real GDP between 2010 and 2011 was

g =15052.4

14779.4− 1 = 0.0185.

To express this growth rate as a percent, multiply 0.0185 by 100 to obtain1.85 percent.

Multi-period growth. The formula above is for the growth rate from periodt to t+ 1. The formula over many periods has a natural extension:

xt+n = (1 + g)nxt,

which follows from repeatedly multiplying x by (1+g) and the first propertyof exponents discussed above. To calculate the growth rate based upon dataon x, one can use the formula

g =

(xt+nxt

)1/n

− 1.

If we want to express this growth rate as a percent, we multiply it by 100.

Example: The FRED database reports that annual US real GDP (mea-sured in 2009 dollars) in 2011 was 15,052.4 billion. Annual US real GDP in1947 was 1,937.6 billion. The average annual growth rate of US real GDPbetween 1947 and 2011 was

g =

(15052.4

1937.6

)1/(2011−1947)

− 1 = 0.0326.

To express this growth rate as a percent, multiply 0.0326 by 100 to obtain3.26 percent.

Note the difference in the average growth rate of 3.26 percent for the USover the post-WWII time period versus the recent annual growth rate of1.85 percent in the previous example.

http://research.stlouisfed.org/fred2/series/GDPC1/downloaddata?cid=106



Continuously-compounded growth rates

For many purposes in this course, it will be easier to use continuously com-pounded growth rates. Mathematically, this device is simply an extensionof the discrete growth rate discussed above when the time interval becomesinfinitesimal. While this growth rate is difficult to conceptualize, it has veryuseful features, which we discuss below.

The continuously compounded growth rate relates variable x across timeperiods as

xt+1 = exp(γ)xt.

Notation note: We will always denote the continuously compounded growthrate as γ.

To compute this growth rate from data on x, one can use the formula

γ = lnxt+1 − lnxt,

which follows from the properties of logarithms listed above. If we wish toexpress this growth rate as a percent, we multiply it by 100.

Example: We can compute the continuously-compounded growth rate us-ing the same data described above. Recall that the FRED database re-ports that annual US real GDP (measured in 2009 dollars) in 2010 was14,779.4 billion. For 2011, annual US real GDP was 15,052.4 billion. Thecontinuously-compounded growth rate is

γ = ln 15052.4− ln 14779.4 = 0.0183.

To express this growth rate as a percent, multiply 0.0183 by 100 to obtain1.83 percent. Note the similarity of the continuously compounded growthrate and the annually compounded growth rate (1.85 percent). This simi-larity is not a coincidence, as we discuss below.

Continuous compounding has three useful features for measuring growthrates:

1. Continuously-compounded growth rates approximate discretely-compounded growth rates. In the example above, the continuously-compounded growth rate and the annually-compounded growth rate arevery similar. The similarity reflects the final property of logarithms listedabove. Specifically,

ln(1 + a) ≈ a when a is small,



where ≈ means “approximately equal to” and the value of a is small (lessthan 0.10 is a good rule of thumb). In words, the logarithm of one plusa is approximately equal to a, when a is small.

In the context of growth rates, take logarithms of both sides of the discretecompounded growth formula [xt+1 = (1 + g)xt] giving us

lnxt+1 = ln(1 + g) + lnxt,

which follows from the first property of logarithms. Rearranging andapplying the approximation discussed above yields

lnxt+1 − lnxt = ln(1 + g) ≈ g when g is small.

Notice that lnxt+1 − lnxt is the continuously compounded growth rate,γ. Putting this information together shows that when the growth rate issmall, the discrete compounded growth rate g will be approximately thesame as the continuously compounded growth rate γ.

2. Continuously compounded growth rates are additive. Supposethat you’re interested in the growth rate of a product xy. For example,x might be the price deflator and y real output, so that xy is nominaloutput. Using our definition:

γxy = ln

(xt+1yt+1

xtyt

)= ln

(xt+1

xt

)+ ln

(yt+1

yt

)= γx + γy.

They add up! Thus, the growth rate of a product is the sum of the growthrates. Mathematically, this result follows from the first two properties oflogarithms discussed above. In the same way, the growth rate of x/yequals the growth rate of x minus the growth rate of y.

This additive feature of continuously compounded growth rates is theprimary reason we use continuous compounding.

3. Averages of continuously compounded growth rates are easy tocompute. Suppose that we want to know the average growth rate of xover n periods:

γ =(lnxt − lnxt−1) + (lnxt−1 − lnxt−2) + · · ·+ (lnxt−n+1 − lnxt−n)

n.

This expression is the average of the one-period growth rates (lnxt −lnxt−1). Now, if you look at this expression for a minute, you mightnotice that most of the terms cancel each other out. The term lnxt−1, forexample, shows up twice, once with a positive sign, once with a negativesign. If we eliminate the redundant terms, we find that the averagegrowth rate is

γ =lnxt − lnxt−n

n.


In other words, the average growth rate over the full period is simply then-period growth rate divided by the number of time periods n.

Example: We can compute the average continuously compounded growthrate for post-WWII GDP data. The average annual growth rate of USreal GDP between 1947 and 2011 was

γ =ln 15052.4− ln 1937.6

2011− 1947= 0.0320.

In percent terms, the average annual growth rate for the US is 3.20 per-cent. Note, again, that because the growth rate is small, its value issimilar to the discretely-compounded growth rate g = 0.0326 calculatedin the previous example.

1.4 Slopes and derivatives

The slope of a function is a measure of how steep it is: the ratio of thechange in y to the change in x. For a straight line, we can find the slopeby choosing two points and computing the ratio of the change in y to thechange in x. For some functions, though, the slope (meaning the slope of astraight line tangent to the function) is different at every point.

The derivative of a function f(x) is a second function f ′(x) that gives us itsslope at each point x if the function is continuous (no jumps) and smooth(no kinks). Formally, we say that the derivative is

∆y

∆x=

f(x+ ∆x)− f(x)

∆x

for a “really small” ∆x. (You can imagine doing this on a calculator orcomputer using a particular small number, and if the number is small enoughyour answer will be pretty close.) We express the derivative as f ′(x) ordy/dx and refer to it as “the derivative of y with respect to x.” The d’sare intended to be suggestive of small changes, analogous to ∆ but with theunderstanding that we are talking about infinitesimal changes.

So the derivative is a function f ′(x) that gives us the slope of a function f(x)at every possible value of x. What makes this useful is that there are somerelatively simple mechanical rules for finding the derivative f ′ of commonfunctions f (see Table 1.1).

Example: Marginal cost. Suppose that total cost c is related to the quan-tity produced q by

c = 100 + 10q + 2q2.


Table 1.1: Rules for computing derivatives.

Function f(x) Derivative f ′(x) Comments

Rules for Specific Functionsa 0 a is a numberax+ b a a, b are numbersaxb baxb−1 a, b are numbersaebx baebx a, b are numbersa lnx a/x a is a number

Rules for Combinations of Functionsg(x) + h(x) g′(x) + h′(x)ag(x) + bh(x) ag′(x) + bh′(x) a, b are numbersg(x)h(x) g(x)h′(x) + g′(x)h(x)g(x)/h(x) [g′(x)h(x)− g(x)h′(x)]/[h(x)]2 h(x) 6= 0g[h(x)] g′[h(x)]h′(x) “chain rule”

Marginal cost is the derivative of c with respect to q. How does it vary withq? The derivative of c with respect to q is

dc/dq = 10 + 4q,

so marginal cost increases with q.

Example: Bond duration. Fixed-income analysts know that prices of bondswith long maturities are more sensitive than those with short maturities tochanges in their yields. They quantify sensitivity with duration D, definedas

D = −d ln p

dy.

In words, duration is the ratio of the percent decline in price (the changein the log) over the increase in yield for a small increase. Two versionsfollow from different compounding conventions. With annual compounding,the price of an m-year zero-coupon bond is related to the yield by p =100/(1 + y)m. Therefore,

ln p = ln 100−m ln(1 + y),

and duration is D = m/(1 + y). With continuous compounding, p =100 exp(−my), ln p = ln 100 − my, and D = m. In both cases, it’s clearthat duration is higher for long-maturity bonds (those with large m).

Example: Marginal product of capital. Suppose that output Y is relatedto inputs of capital K and labor L by

Y = KαL1−α


for α between zero and one. If we increase K holding L fixed, what happensto output? We call the changes in output resulting from small increases inK the marginal product of capital. We compute it as the derivative of Ywith respect to K holding L constant. Since we’re holding L constant, wecall this a partial derivative and write it:

∂Y

∂K= αKα−1L1−α = α

(K

L

)α−1.

Despite the change in notation, we find the derivative in the usual way,treating L like any other constant.

1.5 Finding the maximum of a function

An important use of derivatives is to find the maximum (or minimum) of afunction. Suppose that we’d like to know the value of x that leads to thehighest value of a function f(x), for values of x between two numbers a andb. We can find the answer by setting the derivative f ′(x) equal to zero andsolving for x. Why does this work? Because a function is “flat” (has zeroslope) at a maximum. (That’s true, anyway, as long as the function has nojumps or kinks in it.) We simply put this insight to work.

Fine points. Does this always work? If we set the derivative equal to zero,do we always get a maximum? The answer is no. Here are some of thethings that could go wrong: (i) The point could be a minimum, rather thana maximum. (ii) The maximum could be at one of the endpoints, a or b.There’s no way to tell without comparing your answer to f(a) and f(b).(iii) There may be more than one “local maximum” (picture a wavy line).(iv) The slope might be zero without being either a maximum or a minimum:for example, the function might increase for a while, flatten out (with slopeof zero), then start increasing again. An example is the function f(x) = x3

at the point x = 0. [You might draw functions for each of these problemsto illustrate how they work.] If you want to be extra careful, there areways to check for each of these problems. One is the co-called second-ordercondition: A point is a maximum if the second derivative (the derivative off ′(x)) is negative. While all of these things can happen, in principle, we willmake sure they do not happen in this class.

Example: Maximizing profit. Here’s an example from microeconomics.Suppose that a firm faces a demand for its product of q = 10 − 2p (q andp being quantity and price, respectively). The cost of production is 2 perunit. What is the firm’s profit function? What level of output produces thegreatest profit?


Answer. Profit is revenue (pq) minus cost (2q). The trick (and this isn’tcalculus) is to express it in terms of quantity. We need to use the demandcurve to eliminate price from the expression for revenue: p = (10− q)/2 sopq = [(10− q)/2]q. Profit (expressed as a function of q) is, therefore,

Profit(q) = [(10− q)/2]q − 2q = 5q − q2/2− 2q.

To find the quantity associated with maximum profit, we set the derivativeequal to zero:

dProfit

dq= 3− q = 0,

so q = 3. What’s the price? Look at the demand curve: If q = 3, then psatisfies 3 = 10− 2p and p = 7/2.

Example: Demand for labor. A firm produces output Y with labor L and afixed amount of capital K, determined by past investment decisions, subjectto the production function Y = KαL1−α. If each unit of output is worth pdollars and each unit of labor costs w dollars, then profit is

Profit = pKαL1−α − wL.

The optimal choice of L is the value that sets the derivative equal to zero:

∂Profit

∂L= p(1− α)(K/L)α − w = 0.

(We use a partial derivative here, denoted by ∂, to remind ourselves that Kis being held constant.) The condition implies that

L = K

[p(1− α)

w

]1/α.

You can think of this as the demand for labor: Given values of K, p, and w,it tells us how much labor the firm would like to hire. As you might expect,at higher wages w, labor demand L is lower.

1.6 Spreadsheets

Spreadsheets are the software of choice in many environments. If you’re notfamiliar with the basics, here’s a short overview. The structure is similar inMicrosoft Excel, OpenOffice Calc, and Google documents.

The first step is to make sure that you have access to one of these programs.If you have one of them on your computer, you’re all set. If not, you can


download OpenOffice at www.openoffice.org or open a Google spreadsheetat docs.google.com. Both are free.

In each of these programs, data (numbers and words) are stored in tableswith the rows labeled with numbers and the columns labeled with letters.Here’s an example:

A B C

1 x1 x22 3 253 8 134 5 215

The idea is that we have two (short) columns of data, with variable x1 incolumn A and variable x2 in column B.

Here are some things we might want to do with these data, and how to doit:

• Basic operations. Suppose that you want to compute the natural loga-rithm of element B2 and store it in C2. Then, in C2 you would type:=LN(B2). (Don’t type the period, it’s part of the punctuation of the sen-tence.) The answer should appear almost immediately. If you want to addthe second observation (row 3) of x1 and x2 and put in C3, then in C3you type: =A3+B3. We have expressed functions (LN) and addresses (A3)with upper-case letters, but lower-case letters would do the same thing.

• Statistics. Suppose that you want to compute the sample mean and stan-dard deviation of x1 and place them at the bottom of column A. Then,in A5 type: =AVERAGE(A2:A4). That takes the numbers in column Afrom A2 to A4 and computes the sample mean or average. The standarddeviation is similar: in A6 you type =STDEV(A2:A4). Finally, to com-pute the correlation between x1 and x2, you type (in any cell you like):=CORREL(A2:A4,B2:B4).

If you’re not sure what these functions refer to, see the links to the KhanAcademy videos at the end of this chapter.

1.7 Getting data from FRED

We will use data extensively in this course. One extraordinarily useful source— for this course and beyond — is FRED,

http://research.stlouisfed.org/fred2/,

www.openoffice.org

docs.google.com

http://research.stlouisfed.org/fred2

http://research.stlouisfed.org/fred2/


an online economic database supported by the Federal Reserve Bank of St.Louis. It’s one of the best free tools you’ll ever run across. All of the seriesused in this book are listed in what FRED calls a Published Data List:

http://research.stlouisfed.org/pdl/649,

Names of relevant variables are listed at the end of every chapter.

FRED allows you to graph data, transform it (compute growth rates, forexample), and download it into a spreadsheet. They also have an Excel “add-in” that allows you to download data directly into an Excel spreadsheet.FRED mobile apps allow you to graph data on your phone or tablet.

To get started using FRED, go to the main FRED page and graph USreal GDP (You’ll know what that is shortly.) Click on “Category,” then“National Accounts,” then “National Income and Product Accounts,” then“GDP/GNP,” and finally “Real Gross Domestic Product” (also known asGDPC1). The graph of GDPC1 will then appear with quarterly data be-ginning in 1947:Q1. Notice that recessions are shaded on the graph. Onceyou know the variable code — namely, GDPC1 — you can enter it in theFRED search box on the main page and do this in one step.

If you return to the Category page, you’ll see the wide variety of data thatFRED makes available. Try exploring some of these categories to familiar-ize yourself with popular data series. Each data series has a name (e.g.,GDPC1 for US real GDP). As an exercise, find and graph the consumerprice index (CPIAUCSL), total nonfarm payroll employees (PAYEMS), andthe monthly US/Euro foreign exchange rate (EXUSEU). If you find the cat-egories confusing, simply type what you’re looking for into the search boxon the upper right: “real GDP,” “consumer price index,” and so on.

We have posted a series of FRED tutorials on the NYUSternGE YouTubechannel. In addition to FRED basics, they explain how to format anddownload graphs for course assignments that use FRED. In addition, theSt. Louis Fed offers a series of tutorials that show how to make and alterFRED graphs. You can change the graph type, add data series, changethe observation period or frequency, and transform the data (e.g., percentchange, percent change from a year ago, percent change at an annual rate).You can also alter the graph characteristics (e.g., size, background, color,font, and line style).

http://research.stlouisfed.org/pdl/649

http://research.stlouisfed.org/fred-addin/

http://research.stlouisfed.org/fred-addin/

http://research.stlouisfed.org/fred-mobile/

http://research.stlouisfed.org/fred2

http://research.stlouisfed.org/fred2/categories

http://research.stlouisfed.org/fred2/categories/32992



http://research.stlouisfed.org/fred2/series/GDPC1?cid=106

http://research.stlouisfed.org/fred2/categories

http://www.youtube.com/user/NYUSternGE

http://research.stlouisfed.org/tutorials/fredgraph/


Review questions

If you’re not sure you followed all this, give these a try:

1. Growth rates. Per capita income in China was 439 in 1950, 874 in 1975,and 3425 in 2000, measured in 1990 US dollars. What were the annualgrowth rates in the two subperiods?

Answer. The average continuously compounded growth rates were 2.75percent and 5.46 percent. The discrete (annually compounded) growthrates are 2.79 percent and 5.62 percent, so there’s not much differencebetween them.

2. Derivatives. Find the derivative of each of these functions:

(a) 2x+ 27 [2]

(b) 2x2 + 3x+ 27 [4x+ 3]

(c) 2x2 + 3x− 14 [4x+ 3]

(d) (x− 2)(2x+ 7) [4x+ 3]

(e) ln(2x2 + 3x− 14) [(4x+ 3))/(2x2 + 3x− 14)]

(f) 3x8 + 13 [24x7]

(g) 3x2/3 [2x−1/3 = 2/x1/3]

(h) 2e5x [10e5x]

Answers in brackets [ ].

3. Capital and output. Suppose output Y is related to the amount of capitalK used by

Y = 27K1/3.

Compute the marginal product of capital (the derivative of Y with respectto K) and describe how it varies with K.

Answer. The marginal product of capital is MPK = 9K−2/3 = 9/K2/3,is positive, and falls as we increase K. We call this diminishing returns:The more capital we add, the less it increases output.

4. Find the maximum. Find the value of x that maximizes each of thesefunctions:

(a) 2x− x2 [f ′(x) = 2− 2x = 0, x = 1]

(b) 2 lnx− x [f ′(x) = 2/x− 1 = 0, x = 2]

(c) −5x2 + 2x+ 11 [f ′(x) = −10x+ 2 = 0, x = 1/5]

Answers in brackets [ ].


5. Spreadsheet practice. You have the following data: 4, 6, 3, 4, 5, 8, 5,3, 6. What is the mean? The standard deviation? (Use a spreadsheetprogram to do the calculations.)

Answer. 4.889, 1.616.

6. FRED practice. Use the FRED website to construct the following graphs:

(a) Civilian unemployment rate (UNRATE) from January 1971 throughJuly 2012.

(b) Percent change from a year ago of personal consumption expendi-tures price index (PCEPI) from January 1960 to the present. Whatis the most recent data point?

(c) US Gross Private Domestic Investment (GPDI) as a share of GDP(GDP) from 1960Q1 to the present. What is the most recent datapoint?

(d) Based on these graphs, how are recessions reflected in these threeseries?

Helpful hints: Usually you will be asked to find the data yourself, so youshould familiarize yourself with the various categories of data on FRED.For this exercise, you can find the data by typing the series name (e.g.,PCEPI) into the search box on the FRED website. Doing so will producea simple graph of the entire series. Set the date range using the start andend boxes above the graph. To alter the graph settings, click “GraphSettings.” The dropdown box provides options to change the graph type,font, font size, and other aspects of the graph. Or, you can click “EditData Series 1” to alter the line style, line width, mark type/width, color,frequency, and units. For example, to graph the percentage change froma year ago, change the “Units.”

To graph the ratio of two series, graph the first series and click “AddData Series” and choose “Modify Existing Series.” Search for the secondseries, and click “Add Series.” Under “Edit Data Series 1,” click “Createyour own data transformation,” then type “a/b” in the formula box andclick “Apply.”

If you’re looking for more

If these notes seem mysterious to you, we recommend the Khan Academy.They have wonderful short videos on similar topics, including logarithms(look for “Proof: ln a ...”), calculus (look for “Calculus: Derivatives ...”),and statistics (start at the top). For spreadsheets, the Google doc tutorialis quite good.

http://www.khanacademy.org/#algebra

http://www.khanacademy.org/#calculus

http://www.khanacademy.org/#statistics

https://docs.google.com/support/bin/answer.py?hl=en&answer=140784&topic=20322&rd=1


Symbols and data used in this chapter

Table 1.2: Symbol table.

Symbol Definition

Y OutputK Stock of physical capitalL Quantity of laborg Discrete compounded growth rateγ Continuously compounded growth rateln Natural logarithm (inverse operation of exp)exp Exponential function (inverse operation of ln)f(x) Function of x∆x Infinitesimal change of xf ′(x) Derivative of f(x)dy/dx Derivative of f(x)∂F (x, y)/∂x Partial derivative of F (x, y) with respect to x

Table 1.3: Data table.

Variable Source

Real GDP GDPC1consumer price index CPIAUCSLNonfarm employment PAYEMSUS$/Euro exchange rate EXUSEUUnemployment rate UNRATEPersonal consumption expenditures price index PCEPIGross private domestic investment GPDINominal GDP GDP

To retrieve the data online, add the identifier from the source column tohttp://research.stlouisfed.org/fred2/series/. For example, to retrievereal GDP, point your browser to http://research.stlouisfed.org/fred2/

series/GDPC1

http://research.stlouisfed.org/fred2/series/

http://research.stlouisfed.org/fred2/series/GDPC1


2Macroeconomic Data

Tools: GDP; accounting identities; price and quantity indexes.

Key Words: GDP; value added; real; nominal; index; deflator.

Big Ideas:

• GDP is three things at once: production (value added by productionunits), income (payments to labor and capital), and expenditure (con-sumption, investment, government spending, net exports).

• Current price variables (such as nominal GDP) can be decomposed intomeasures of price and quantity. There are several ways to do this, butnone of them are perfect.

Gross Domestic Product (GDP) is our primary measure of macroeconomicperformance: the total value of output produced in a particular economyover some period of time (typically a year or a quarter). Countries with highGDP per person are said to be rich, and those in which GDP has gone downare said to be in recessions. But what is GDP and how is it measured? Wereview its definition and construction below. Along the way, we also noteconnections among output, income, and expenditures, and explain how weseparate changes in quantities from changes in prices.

The system that produces GDP and related numbers is known as the Na-tional Income and Product Accounts (NIPA). The national accounts areanalogous to financial statements: They give us a picture of an economy,just as financial statements give us pictures of firms. Similar methods areused in most countries, so the numbers are (in principle) comparable.

19


2.1 Measuring GDP

GDP is the total value of goods and services produced in a given region,typically a country. In the US, for example, GDP was 15,533.8 billion USdollars in 2011: 15.5 trillion dollars. With a population of 312 million(average for the year), that amounts to nearly $50,000 per person. Butwhere does this number come from? What does it mean?

The standard approach to measuring GDP is to add up the value producedby every firm or production unit in the economy. The question is how weseparate value produced by one firm from value produced by another in aneconomy in which the value chain typically involves many firms. Walmart,for example, has enormous sales, but most of the value is already built intoproducts by suppliers. As a concrete example, consider a fictional firm thatassembles PCs from parts made elsewhere. Its only other expense is labor.Let’s say that the firm’s income statement looks like Table 2.1.

The question is how we measure this firm’s contribution to output. Thestraightforward answer is 40m, the total value of its sales. But if we thinkabout this a minute, we realize that 6m of this was produced somewhere else,so it shouldn’t be counted as part of the firm’s output. A better answer is34m, the value the firm has added to the parts. That, in fact, is the acceptedanswer: We base GDP on value added , not on sales. To get GDP for thewhole economy, we sum the value added of every production unit.

Another way to compute value added is to sum payments to labor andcapital. In this case, we add 20m paid to workers (labor) to 14m net incomepaid to owners of the firm (capital). That gives us total payments of 34m, thesame number we found above using a different method. Since this approachis based on the income received by labor and capital, we see that the valueof production and income are the same. More on this in the next section.

Usually, when we compare the GDPs of two countries, we presume thatthe country with the larger GDP produces more in some useful sense. But

Table 2.1: PC assembler’s simple income statement.

Sales revenue 40,000,000

Expenses 26,000,000Wages 20,000,000Cost of goods sold (parts) 6,000,000

Net Income 14,000,000

2. Macroeconomic Data 21

suppose that they produce different goods: Country A produces 10 billionapples and country B produces 10 billion bananas. Which produces more?We generally assume that if apples are worth more than bananas, thencountry A produces more. The idea is that market prices tell us whichgoods are more valuable, apples or bananas. The same idea underlies ourmeasurement of value added.

To make this concrete, suppose the 40m sales of our fictitious company con-sists of 20,000 PCs at $2,000 each. Our presumption is that the market priceof $2,000 reflects economic value, and we use it as part of our calculationof GDP. In some cases, this isn’t so obvious. In, say, North Korea, pricesdo not generally reflect market forces, so it’s not clear how we would calcu-late economic value. There are also some subtle issues in market economiesabout how to value non-market activities, such as washing your own clothes,and “bads,” such as pollution. Typically, neither is valued in the nationalaccounts. We don’t claim this is right, but it’s what we do.

Example (salmon value chain). A fisherman catches a salmon and sells itto a smokehouse for $5. After smoking it, the smokehouse sells it to Fairwayfor $10, which, in turn, sells it to a restaurant for $15. The same restaurantbuys lettuce from a farmer at Union Square for $3. The restaurant puts thelettuce and salmon together on a plate and sells it to an NYU student for$25. How much does each production unit contribute to GDP? What is theoverall contribution to GDP?

Answer. The contributions (value added) are $5 each for the fisherman,smokehouse, and Fairway, $3 for the farmer, and $7 for the restaurant, fora total of $25.

Note that we could have computed GDP by counting only the value of thefinal good in the value chain. This is true in general: GDP can be computedas the total value of final goods produced in the economy. Intermediateproducts (salmon, lettuce, PC parts) must then be ignored, as their valueshows up at the end of the value chain.

We’ll finish this section with two subtle issues. One is the treatment ofgovernment services. We generally treat government as a producer of valueadded and measure its output at cost. If we pay the mayor $100,000, that’scounted as $100,000 of value added whether she does a good job or not. Theother is that capital expenditures are not treated as intermediate inputs.Basically, we ignore them when we compute the value added of a firm.Why? Because the expense is balanced by an equal addition to the firm’svalue. With firms, financial statements do something similar: We spreadthe expense out over time in the form of depreciation. Here, we measure


Table 2.2: PC assembler’s complicated income statement.

Sales revenue 40,000,000

Expenses 32,000,000Wages 20,000,000Cost of goods sold 6,000,000Interest 2,000,000Depreciation 4,000,000

Net income 8,000,000

output gross of depreciation, so we ignore capital expenditures altogether asexpense. It sounds a little strange, but that’s what the national income andproduct accounts do.

2.2 Identities

Since every transaction has both a buyer and a seller, we can often approachany measurement problem from (at least) two directions. This gives rise toidentities: relations that hold as a matter of accounting truth. They donot depend on any particular economic theory and, for that reason, areextremely useful.

Income (Gross Domestic Product = Gross Domestic Income).We’ve seen the first identity already: output and income are equal. Let’s goback to our PC assembler to see this in action, adding a few things to makethe example more realistic. In Table 2.2 we add two new expenses, interestand depreciation. These categories are counted as capital income. In theprevious section, we computed (its contribution to) GDP as value added of34m. Here, we compute GDI (I for Income) from payments to labor (20m)and capital (14m). Capital payments include the net income paid to own-ers of the firm, interest income paid to the debt holders, and depreciation.Adding labor income and capital income, we arrive at GDI of 34m. Theanswer, of course, is the same.

Since we include depreciation in our measures of output and income, we referto them as gross — gross of depreciation. In principle, we could computeNet Domestic Product by subtracting depreciation, but most people stickwith GDP because economic depreciation (as opposed to what shows up onfinancial statements and tax returns) is difficult to measure.

The national income and product accounts do this at the aggregate level:namely, measure output by adding up payments to inputs. By construc-tion, then, output and income are the same. To give you a sense of real


numbers look like, we report the income for the US economy in Table 2.3.The statistical discrepancy is a reminder that the measurement system isn’tperfect.

Table 2.3: Income components of US GDP.

Compensation of employees 9,258.4Proprietor’s income 1,346.7Corporate profits 1,654.7Rental income 610.8Net interest income 678.0Taxes and miscellaneous 1,264.8Depreciation 2,746.7

Gross domestic product 17,560.1Statistical discrepancy -212.0

The numbers are for 2014, billions of US dollars, from theBEA’s NIPA Table 1.10.

Expenditures (Gross Domestic Product = Gross Domestic Expen-diture). Our second identity comes from the perspective of expenditureson final goods—the last stage in the value chain. We distinguish both whobuys them (consumers, firms, governments, or foreigners) and whether theyare consumption or investment. The most common decomposition of thissort is: GDP equals consumer expenditures C by households plus businessand residential investment I plus government purchases of goods and ser-vices G plus net exports NX ; in more compact notation,

Y = C + I +G+ NX . (2.1)

We refer to this as the expenditure identity . On the left, Y is the letter weuse for GDP. (It’s not clear where the letter Y comes from, but we followa long tradition in using it this way.) On the right are the expenditurecomponents of GDP. The point is that the two are equal: Everything that’sproduced is sold — to someone. (And if it’s not sold, we call it an additionto inventories and include it in I. The idea is that firms produce the outputand sell it to themselves.)

We refer to C as (personal or household) consumption. Investment (I)is primarily accumulation of physical capital by firms: purchases of newbuildings and machines, plant and equipment in the language of nationalincome accountants (two-thirds of the famous PPE and capex of financialaccounting ). It also includes new housing construction. In some sources,the sum of construction outlays and spending on equipment and softwareis referred to as “gross fixed capital formation.” Investment also includes,

http://www.bea.gov/iTable/iTableHtml.cfm?reqid=9&step=3&isuri=1&903=51


as noted, additions to the stock of inventories, a category that is small, onaverage, but highly variable.

Government purchases G consist of spending on goods and services (mainlywages) for both consumption and investment purposes. They do not includegovernment outlays for social security, unemployment insurance, or medicalcare. We think of them, instead, as transfers since no goods or services areinvolved. It also omits interest payments on government debt, which wetrack separately. Net exports (NX ) are exports minus imports: the tradebalance, in other words.

Some recent numbers for the US are reported in Table 2.4.

Table 2.4: Expenditure components of US GDP.

$ billions Percent of GDP

Consumption 11,865.9 68.4%Durable goods 1,280.2Nondurable goods 2,668.2Services 7,917.5

Gross private investment 2,860.0 16.5%Nonresidential 2,233.7Residential 549.2Change in inventories 77.1

Government consumption 3,152.1 18.2%Net exports of goods and services −530.0 −3.1%

Exports 2,341.9Imports 2,871.9

Gross domestic product 17,348.1 100.0%

The numbers are for 2014, from the BEA’s NIPA Table 1.1.5.

Example (salmon value chain, continued). Suppose, in our example,that the salmon is imported from Norway. Then you’d think — and you’dbe right — that it shouldn’t count as US GDP. How does that work?

On the income side of the accounts, the contributions to GDP are the sameas before: the contributions are $5 each for the fisherman, smokehouse, andFairway, $3 for the farmer, and $7 for the restaurant, for a total of $25. Butwhen the salmon is imported, $5 is attributed to Norway’s GDP and only$20 to US GDP.

What if we looked at this from the perspective of expenditures on finalgoods? The final sale ($25) is the same as before, but the imported salmon



is now subtracted to give us a contribution to GDP of $20. Why subtracted?You’ll recall that we needed to subtract imports from GDP, because pur-chases of imported goods do not reflect local production. That’s what netexports does in the expenditure identity: it’s a correction for the differencebetween production and expenditures.

Flows of funds. The expenditure identity follows the goods, but youcan also follow the “money” (the financial funds) that goes along with thegoods. For households, you might think about how income compares toconsumption. If it’s higher, we call what’s left saving, which is a source offunds that can be used by others. We might also think about how firmsfinance investment in new plant and equipment. They might, for example,raise funds in capital markets from households.

Let’s be specific. We’ll look at two similar relations, both based on theexpenditure identity. One is

S = Y − C −G = I + NX, (2.2)

where S is (gross domestic) saving. This is a consolidated measure ofsaving in which we subtract both household and government expendituresfrom income. It’s also a gross measure since income (GDP) includes depre-ciation. Investment is also gross, so the two sides of the relation balance.The other relation separates household and government activities:

Sp + Sg ≡ (Y − T − C) + (T −G) = I + NX,

where T is taxes collected by the government net of transfer payments andinterest, Sp = Y − T − C is (gross) private saving; and Sg = T − G isgovernment “saving” (the negative of the government deficit). Clearly, Spand Sg are two components of national saving S. Most countries reporta further breakdown of saving by households, governments, and firms, butthis will be enough for us.

We refer to both versions as flow of funds identities. What do they tell us?Roughly speaking, the left side is a source of funds and the right a use offunds, and sources and uses balance. In the first version, saving is a source offunds that can be used to purchase corporate securities (which finance firms’new investment in plant and equipment) or foreign securities (which financea trade deficit by the rest of the world if NX is positive). If net exportsare negative, it’s the reverse, of course: We sell securities to the rest of theworld, which is then a source of funds. In the second version, householdsaving can also be used to purchase government securities (if governmentsaving is negative).


Example (PC assembler, continued). Suppose that 10m of the 40min sales are sold abroad. If this is the only firm in the economy, what areY , NX , C, and S? Assume that investment and the government deficit arezero.

Answer. GDP remains 34m: production hasn’t changed. Net exports equalexports (10m) minus imports (6m) or 4m. With no investment or govern-ment deficit, the 30m of local sales must be consumption. Saving is, there-fore, 4m = 34m – 30m (income minus consumption). The flow-of-fundsidentity then tells us that saving of 4m is used to purchase 4m in foreignsecurities. Stated differently, the rest of the world (everyone but us) musthave a trade deficit of 4m, which they finance by borrowing from us (thesaving we mentioned).

2.3 Distinguishing prices from quantities

You’ll see various versions of the terms real and nominal GDP. NominalGDP measures output in dollars (or local currency units), and real GDPmeasures the quantity of output once overall changes in prices have been(somehow) taken out.

A price index or deflator is a measure of the overall level of prices — what wecall the price level . If the price level rises over time, we say that the economyexperiences inflation; if the price level decreases, the economy experiencesdeflation.

The question for this section is how we separate changes in quantities (realGDP growth) from changes in prices (inflation). The former is good (wehave more stuff), but the latter is bad (prices are going up), so it makessome difference to us which we have. Like sales, GDP and related objectsare values: products of price and quantity. You might well ask: How muchof a change in value is a change in quantity, and how much a change in price?With one product, the answer is easy. With more than one, you need toaverage the prices or quantities somehow, and (sad to say) there’s no obviousbest way to do this. There are, instead, many ways to do it, and they giveus different answers. We’ll charge ahead anyway, but it’s something to keepin mind.

One difficulty in separating prices and quantities is that prices of specificproducts change in different ways, and it’s not clear how to average them toget a measure of “overall” prices. Two sensible approaches, known as fixed-basket and fixed-weight, respectively, give different answers. In practice,this isn’t a huge problem (the answers usually aren’t much different), but


it adds another element of fuzziness to macroeconomic data. The issue isthat the economy has many goods and services whose prices and quantitieschange by different amounts over time. If all prices rose by ten percentbetween last year and this year, we would say that inflation is ten percentand divide this year’s nominal output by 1.10 to get real output. But whenprices of different products change by different amounts, things aren’t thateasy.

The consumer price index (CPI) is based on a fixed-basket approach whichmeasures the change in the price level as the change in the total cost ofa given basket of products (two quarts of milk, one hamburger, five news-papers, etc). The difficulty here is that people change what they consumeover time, partly in response to price changes and partly because tastes andproducts change. Should we use last year’s typical basket or this year’s?The GDP deflator is based on a fixed-weight approach, and is constructedin two steps. We first compute a measure of real GDP by evaluating (typi-cally different) expenditure quantities at constant prices. The price deflatoris then the ratio of nominal to real GDP. The difficulty is, again, that priceschange over time. So, should we use last year’s prices or this year’s?

Fixed-basket approach. The CPI indicates the change in the total cost ofa basket of goods and services that is representative of a typical household’sspending habits at a given date. Such a basket might include, say, five gallonsof gasoline, one haircut, two pounds of chicken, three bottles of soda, andso on. Government statistical agencies do this by sending people to storesto check the prices of all the products in the basket. The CPI is the costof the whole basket, normalized to equal 100 at some date. It’s the sameidea, really, as the Dow Jones Industrial Average or the S&P 500. Producerprice indexes apply a similar methodology to goods purchased by firms. Anexample shows how the fixed-basket approach works.

Example (fish and chips). Consider an economy with two goods, fishand chips. At date 1, we produce 10 fish and 10 chips. Fish sell for 25 centsand chips for 50 cents. At date 2, the prices of fish and chips have risen to50 cents and 75 cents, respectively. The quantities have changed to 8 and12. We summarize the data in Table 2.5.

Table 2.5: Price and quantity data.

Chips Fish

Date Price Quantity Price Quantity

1 0.5 10 0.25 102 0.75 12 0.50 8


Note that the two prices have not gone up by the same amount: the price offish has doubled, while chip prices have gone up by only 50 percent. Anotherway to say the same thing is that the relative price of chips to fish has fallenfrom 2 (= .50/.25) to 1.5 (= .75/.50). What is the inflation rate?

Table 2.6: consumer price index computation.

Date CPI

1 7.50 = .50× 10 + .25× 102 12.50 = .75× 10 + .50× 10

Answer. We construct the CPI using date 1 quantities. The index is shownin Table 2.6.

The inflation rate by this measure is π = 12.50/7.50− 1 = 0.667 = 66.7%).Since nominal GDP growth is 73.3 percent, real GDP growth is 4 percent:

gY =1 + gPY

1 + π− 1 =

1 + 0.733

1 + 0.666− 1 = 0.04.

By convention, the CPI in the base year (year 1 in this case) is normalizedto 100. Normalizing is straightforward: Just divide all the values of the CPIby its value in the base year and multiply by 100. In our example, the indexis 100 in year 1 and 166.7 in year 2.

Fixed-weight approach. Price deflators are typically computed from theratio of GDP (or one of its other expenditure components) at current- andbase-year prices (these are called nominal and real GDP.) Over several peri-ods, this fixed-weight approach applies a constant set of prices to changingquantities. As before, this is easiest to see in an example.

Example (fish and chips, continued). We compute GDP at currentprices and date 1 prices in Table 2.7. The GDP deflator (the ratio of nominalto real GDP) is 1.0 in year 1. This is trivial, as nominal and real GDPmust coincide in the base year. In year 2, the deflator is 1.625 = 13/8,implying an inflation rate of 62.5 percent. Note the difference from theinflation rate computed with the CPI. In short, different approaches lead to

Table 2.7: Nominal and real GDP computation.

Date Nominal GDP (current prices) Real GDP (date 1 prices)

1 $7.50 (= .50× 10 + .25× 10) $7.50 (= .50× 10 + .25× 10)2 $13.00 (= .75× 12 + .50× 8) $8.00 (= .50× 12 + .25× 8)


different measures of inflation. The conceptual difficulty with both methodsis that it’s not clear how to measure the price level when relative prices arechanging. What can we do? We content ourselves with the knowledge thatthe differences are typically small and remind ourselves that macroeconomicmeasurement (like financial accounting) is as much art as science.

2.4 Fine points

Some other issues you may run across:

Causality. You might be tempted to interpret identities as saying that oneside of an identity causes the other. Don’t be. For example, you mighthear someone say that low consumption is causing low output (“We needconsumers to spend more.”). However, the identity says only that if outputgoes down, then so must one or more of its components. No causalityis implied. We could as easily say that consumption falls because outputdid. The point is not that there is no causal connection, but that no suchconnection is built into the identity.

Underground economy. Standard GDP figures do not include the valueof goods and services produced by the so-called “underground” economy.This term generally refers to businesses that are not licensed to operate,such as sellers of counterfeit CDs in the streets of Bangkok, and businessesevading either income or social security taxes, such as Southern Spain’s farmsemploying illegal immigrants as day laborers. Such activity is generally notreported and, therefore, does not show up in official statistics. In advancedeconomies such as the US and Japan, the size of the underground economy isthought to be small. But in developing countries, such as Peru and Lebanon,it has been estimated to be as large as 50 percent of official estimates of GDP.

Capital gains. We’ve seen that GDP reflects income, but there are kindsof income that are not included in GDP. The prime example is capital gains.They are part of your income, but do not show up in GDP because they donot reflect (at least not directly) the production and sale of current output.And since they’re not in GDP, they’re not in saving either. One curiousresult is that net worth can rise even when saving is zero. In the US, capitalgains are a larger fraction of changes in net worth than saving. For similarreasons, GDP does not include interest on government debt. Why? Becauseit isn’t a payment made for producing goods and services.

GDP v. GNP. While GDP measures output produced within the bor-ders of a given country, Gross National Product (GNP) measures outputproduced by inputs owned by the citizens of that country. For example,


to compute Bangladesh’s GNP, we need to add to GDP the income paidto Bangladeshi capital invested abroad and subtract income paid to capitalinstalled in Bangladesh but owned by citizens of other countries. Similarly,with labor, we need to add the wages earned abroad by Bangladeshi peopleand subtract the wages earned in Bangladesh by foreign nationals. Thus,GNP is a measure of the income received by “locally-owned” labor and cap-ital. In most countries, the differences between GDP and GNP are small.One exception is Ireland, where a large amount of foreign capital makes GNPsignificantly smaller than GDP (by about 20 percent last time we looked).

Net exports vs. current account. You may hear people refer to theUS “current account” deficit. What are they talking about? The currentaccount (we’ll label this CA later in the course) is net exports (the tradebalance) plus net receipts of foreign capital and labor income plus miscella-neous transfers from abroad. In the US, there’s usually little difference, butIreland is a different story. We’ll generally use the terms current account,net exports, and trade balance as synonyms. Current account sounds a littlecooler; you can use it to make people think you’re an expert.

Chain weighting. The US — and many other countries, too — now usesa method that’s somewhere between fixed-weight and fixed-basket methods:chain-weighting. It mitigates some of the problems of applying the sameprices over long periods of time (when relative prices often change dramat-ically), but doesn’t eliminate them. If we told you exactly what it is, youreyes would glaze over. But trust us, it’s an improvement.

Prices and quality change. Many people feel that price indexes do notadequately account for increases in product quality. As a result, price in-creases are (slightly) overstated, and quantity increases are understated.Separating prices from quantities is particularly difficult with services be-cause the quantity produced is inherently difficult to measure. (It soundslike the start of a joke: How can you tell when a lawyer is more productive?)Our best guess is that this adds less than 1 percent to the inflation rate:that is, inflation is probably 0.5 percent to 1 percent lower than reported.Not a lot, but it adds up over time.

Expenditure deflating. In most countries, real GDP is computed byapplying price deflators to final goods, typically using the expenditure com-ponents. This isn’t real GDP; it’s real GDE (gross national expenditure).The two are often similar, but need not be if production is largely exported.As an extreme example, Saudi Arabia produces oil for export. If we adjustGDP for changes in prices of Saudi purchases (food, shelter, imported cars,and electronic equipment), then an increase in the price of oil can lead to anincrease in real GDP, even if the quantity of oil produced hasn’t changed.


An alternative is to adjust production quantities directly for price changes,which some countries do.

PPP-adjusted data. When we compare output across countries, peoplehave noticed that if (say) the euro increases in value relative to the dollar,then it appears that Europeans have become richer than Americans. Wesay “appears” because we haven’t taken into account that dollar prices ofnon-tradable goods, such as, haircuts and car-washes, are typically higherin Europe when the euro is strong. In other words, this is a change inprices, not quantities. A similar issue arises when comparing GDPs of a richcountry such as Germany, and a developing country, such as Botswana. Ifwe use local prices and simply convert them to dollars or euros at the spotexchange rate, Botswana will look poorer than it actually is because localprices of many basic goods are much lower in Botswana. The state-of-the-art way to address this issue is to apply the same prices to output in bothlocations to produce real GDP based on “purchasing power parity” (PPP).The logic is the same as with the GDP deflator, but the comparison is acrosscountries rather than across time.

Seasonal adjustment. Quarterly or monthly data often exhibit sys-tematic variations by season. Quarterly GDP, for example, typically has asharp increase in the fourth quarter (holidays). Most macroeconomic datahave been smoothed to eliminate this seasonal variation. The same thinghappens with business data: Analysts often report changes relative to thesame period the year before, which will help eliminate any seasonal effect.

Revisions. NIPA data are revised frequently and significantly. The “ad-vance estimate” of real GDP is released in the first month following eachquarter (month t, say). The fourth quarter estimate, for example, is re-leased in late January. This estimate is revised in each of the next twomonths (months t+ 1 and t+ 2) as additional data becomes available. Sub-sequent revisions occur annually, as more new data (such as tax revenues)appears and as seasonal factors are updated. In addition, roughly every fiveyears, a benchmark revision updates the base year for calculating real GDP.The current base year of 2009 was established in the July 2013 benchmarkrevision. Benchmark revisions also typically include technical improvementsin the measurement of past economic activity. For example, the 2013 bench-mark altered NIPA history all the way back to 1929. The idea was to capturemore accurately the impact of R&D on investment, in addition to other lesssignificant modifications.

NIPA revisions matter greatly to business decision makers and governmentpolicymakers who are making decisions in real time. It’s an unfortunate factof life that they’re working with imperfect information. The standard devi-ation of revisions between each of the initial real GDP releases (in months


t, t+ 1, and t+ 2) and the most recent estimate was 1.6% for the 1983-2009period. This represents a sizable uncertainty about the current state of theeconomy. It means that economic forecasters must first “backcast” GDPrevisions.

By way of example, consider economic activity in the third quarter of 1990as contemporary observers viewed it. The initial report of third-quarter1990 real GDP showed quarter-to-quarter annualized growth of 1.8%. Twoyears later, the revised reading showed a decline of 1.6%. With the benefitof hindsight, the National Bureau of Economic Research Business CycleDating Committee estimates that a mild recession began in July 1990, butNIPA data released in 1990 and 1991 did not show it. Moreover, the FederalReserve did not respond by easing monetary policy until the fourth quarterof 1990. As of August 2015, the latest estimate for the third quarter of 1990was a change of 0.1%.

Executive summary

1. GDP measures the total value of production measured at market prices,the sum of value-added by every production unit in the economy.

2. Identities.

• Output (GDP) = Income (payments to labor and capital, gross ofdepreciation).

• Output (GDP) = Expenditures (purchases of goods): Y = C+I+G+NX

• Flow of funds (How is investment financed?): S = I + NX

3. We use magic to separate changes in quantities from changes in prices:

• Quantity indexes, such as real GDP, measure the overall movement ofquantities.

• Price indexes measure the overall movement of prices.

Review questions

1. Value added. Company A sells four tires to Company X for $400. Com-pany B sells a CD player to Company X for $300. Company X installsboth in a car, which it sells for $5000. What is the total contribution toGDP of these transactions?

Answer. The contribution to GDP is $5000: $400 from A, $300 from B,and the rest from X.


2. Expenditures. Place each transaction into the appropriate expenditurecomponent of US GDP:

(a) Boeing sells an airplane to the Air Force.

(b) Boeing sells an airplane to American Airlines.

(c) Boeing sells an airplane to Virgin Atlantic airline.

(d) Boeing sells an airplane to Halle Berry.

(e) Boeing builds an airplane but fails to sell it.

(f) Airbus sells a plane to Delta Air Lines.

Answer.

(a) G: It’s a government purchase, as the Air Force is part of the FederalGovernment.

(b) I: It’s investment, as American Airlines will use the aircraft as capitalgood.

(c) NX: It’s export, since Virgin Atlantic is incorporated in the UnitedKingdom.

(d) C: It’s consumption (durable consumption), because Halle Berry willuse the plane for her personal travel.

(e) I: It’s investment, because the plane will increase Boeing’s inventoryof unsold products.

(f) I and −NX: It’s an investment and an import, so the net is zero.

3. Prices and quantities. The following data describe the NYU economy:

Prices Quantities

Year PCs Pizza Beer PCs Pizza Beer

2000 100 10 5 25 100 2502005 50 20 15 50 125 2002010 25 30 30 100 150 150

(a) Compute real and nominal GDP and the GDP deflator using 2000as the base year.

(b) Compute the CPI using 2000 quantities as your basket.

Answer. The numbers are

Year Nominal GDP Real GDP Deflator CPI Base = 100

2000 4750 4750 100.00 4750 100.002005 8000 7250 110.34 7000 147.372010 11500 12250 93.88 11125 234.21


The point is that different methods give different answers. This is moststriking if we compare the fourth and last columns. The last one is theCPI, indexed so that it’s value is 100 in 2000. Note that the deflatorhas prices going down in 2010, and the CPI has prices rising—a lot! Thereason is that the CPI has a fixed basket and doesn’t account for thesubstitution effect: our tendency to buy more PCs as their price falls.

4. Investment and depreciation. This problem was suggested by FredericBouchacourt, MBA 09. The issue is how we deal with investment anddepreciation; we need to make sure that they show up in output, expendi-tures, and income in the same way so that we get the same GDP numberall three ways. Imagine an economy with three companies, named D, E,and F, which operate over years 1 and 2 as follows:

• D produces apples and sells them to F for $10 in years 1 and 2. This$10 is paid to workers.

• E builds a machine to can apples and sells it for $10 to F in year 1 anddoes nothing in year 2. It pays its workers $10 in year 1, nothing inyear 2.

• F buys apples from D for $10 in years 1 and 2 and buys a machine tocan apples from E for $10 in year 1. F pays its workers $10 each year.With the help of this machine, F produces canned apples in years 1 and2 that are sold to final consumers for $30 in each year. The machineis amortized equally over the two years: $5 per year.

In this economy:

(a) What is GDP in years 1 and 2?

(b) What are consumption and investment?

(c) What are capital and labor income?

(d) What is net domestic product in each year (GDP minus deprecia-tion)?

Answer.

(a,b) We can find GDP two ways: as value added (summed across produc-ers) or as expenditures (summed across categories). If we computevalue added for each firm and sum, we have

Year 1 Year 2

Firm D 10 10Firm E 10 0Firm F 20 20

GDP 40 30


Note that investment does not count as part of the cost of mate-rials: That’s the way the national accounts work. It’s similar tofinancial accounting in that we don’t consider new plant and equip-ment (“capex”) an expense, although we may include depreciationof existing capital. The latter doesn’t show up here because wemeasure output gross of depreciation.

If we look at the expenditure identity, we have consumption C of$30 each year (canned apples) and investment I of $10 in the firstyear only. Expenditures add to $40 the first year, $30 the second,so we get the same answer.

(c) Value added is payments to capital and labor. Since we know valueadded and payments to labor, payments to capital are the difference.Payments to labor are $30 in year 1, $20 in year 2. In year 1, capitalreceives (10 − 10) + (10 − 10) + (20 − 10) = $10, of which $5 isdepreciation. In year 2, capital receives (10−10)+0+(20−10) = $10,of which $5 is depreciation.

(d) Net domestic product is GDP minus depreciation. Since deprecia-tion is 5 each year, NDP is $35 (=40–5) the first year, $25 (=30–5)the second. Effectively, we’ve subtracted off the cost of the invest-ment, but unlike other material costs, we do it over time rather thanall at once. That’s the logic of amortization: to spread the cost overtime, since the benefits are presumably spread the same way. Youcan also calculate net domestic income just as we did gross domesticincome, except that you subtract depreciation from capital incomeeach period. That way, net domestic product equals net domesticincome.

5. Real-world data. Find the appropriate data for US income and expen-ditures from the Bureau of Economic Analysis (BEA) online interactivetables, particularly Tables 1.10 and 1.1.5.

(a) What are the expenditure components of GDP? How does the officialversion differ from ours? What is the share of consumption in GrossDomestic Product?

(b) What are the components of Gross Domestic Income? How doesthe official version differ from ours? What is the share of laborcompensation in Gross Domestic Income?

(c) Are Gross Domestic Product and Gross Domestic Income the same?Why or why not?


Most macroeconomics textbooks cover similar material. If you’re interestedin how measurement issues affect international comparisons, here are some

http://www.bea.gov/iTable/iTable.cfm?ReqID=9&step=1#reqid=9&step=1&isuri=1

http://www.bea.gov/iTable/iTable.cfm?ReqID=9&step=1#reqid=9&step=1&isuri=1




particularly interesting papers on the subject:

• Ben Bernanke, “Economic measurement,” relates GDP to measures of“economic well-being” and “happiness.”

• Rob Feenstra, Hong Ma, Peter Neary, and Prasada Rao, “Who shrunkChina?” describe the impact of various measurement issues on estimatesof China’s GDP.

• Chad Jones and Pete Klenow, “Beyond GDP,” look at the relation be-tween GDP per person and various other measures of individual welfare.



Symbol Definition

Y Gross domestic product (= Expenditure = Income)C Private consumptionI Private investment (incl. residential and business investment)G Government purchases of goods and services (not transfers)X ExportsM ImportsNX Net exports (= X −M)S Gross domestic saving (= Y − C −G = I +NX)Sp Private saving (= Y − T − C)Sg Government saving (= T −G)T Taxes collected net of transfer payments and interestπ = gP Discretely-compounded growth rate of price index (inflation)gY Discretely-compounded growth rate of real GDPgPY Discretely-compounded growth rate of nominal GDP

http://www.federalreserve.gov/newsevents/speech/Bernanke20120806a.htm

http://papers.nber.org/papers/w17729

http://papers.nber.org/papers/w17729

http://klenow.com/Jones_Klenow.pdf



Variable Source

Nominal GDP GDPCompensation of employees GDICOMPProprietor’s income PROPINCCorporate profits after tax W273RC1Q027BEATaxes on corporate profits A054RC1Q027SBEAGross domestic income GDIRental income RENTINDepreciation COFCConsumption PCEDurable goods PCDGNondurable goods PCNDServices PCESVGross private domestic investment GPDINonresidential investment PNFIResidential investment PRFIChange in inventories CBIGovernment consumption GCENet exports of goods and services NETEXPExports EXPGSImports IMPGSGross private savings GPSAVEGross government savings GGSAVEGDP deflator GDPDEFConsumer price index CPIAUCSLNominal GNP GNPCurrent account BOPBCA

To retrieve the data online, add the identifier from the source column to http:

//research.stlouisfed.org/fred2/series/. For example, to retrieve nominal GDP,point your browser to http://research.stlouisfed.org/fred2/series/GDP



http://research.stlouisfed.org/fred2/series/GDP


Part IILong-Term Economic Performance

39

Long-Term Overview

This outline covers key concepts from the first part of the course: long-term economic performance. It is not exhaustive, but is meant to help you(i) anticipate what is coming and (ii) organize your thoughts later on.

The Aggregate Production Function

Tools: Cobb-Douglas production function.

Key Words: Productivity (TFP); constant returns to scale, diminishingmarginal product, capital, labor.

• A production function relates output (real GDP) to inputs (capital andlabor). Ours have three essential properties: (i) more inputs lead to moreoutput; (ii) diminishing returns to capital and labor; (iii) constant returnsto scale.

• The Cobb-Douglas production function is a specific form that we’ll usethroughout.

• Total factor productivity (TFP) is the overall efficiency with which inputsare transformed into outputs.

The Solow Model

Tools: Capital accumulation dynamics; Cobb-Douglas production function.

Key Words: Investment; saving; depreciation; steady state; convergence.

41


Big Ideas:

• The Solow model connects saving and investment with economic growth.

• In the Solow model without productivity (TFP) growth, capital accu-mulation does not generate long-run growth. The reason is diminishingreturns to capital: the impact of additional capital declines the more youhave. As a result, differences in saving rates have only modest effects onoutput per worker and none at all on its long-run growth rate.

• TFP growth generates long-run growth in output per worker.

Sources of Economic Growth

Tools: Cobb-Douglas production function; level and growth accounting;continuously-compounded growth rates.

Big Ideas:

• Level and growth accounting allow us to quantify the sources of growth:the contributions of capital, labor, and total factor productivity (TFP) togrowth in real GDP.

• TFP accounts for most of the cross-country differences in output perworker and in differences in the growth rate of output per worker.

Institutions and Policies

Key Words: Institutions; governance; time consistency; property rights;markets.

Big Ideas:

• Cross-country differences in productivity (TFP) are connected to differ-ences in institutions that shape productivity and policy.

• Good institutions include good governance; time consistency; rule of law;property rights; open and competitive markets.

Labor Markets

Tools: Labor supply and labor demand diagrams; simple model of un-employment dynamics.

Key Words: Labor force; employment; unemployment; vacancies; acces-sions and separations.

43

Big Ideas:

• Employment and unemployment rates summarize the labor market statusof the adult population.

• Labor market institutions and policies affect employment, unemployment,and job creation.

• Unemployment and vacancy rates tell us about excess supply and demandin labor markets. Unemployment arises from the time it takes to matcha worker and with an appropriate job and firm.

Financial Markets

Key Words: Time consistency; information asymmetry.

Big Ideas:

• Effective financial markets require strong institutional support.

• Good institutions deal with information asymmetries and time consistencyissues.

International Trade

Tools: Ricardo’s model of trade; consumption and production possibilityfrontiers.

Key Words: Absolute advantage; comparative advantage; autarky.

Big Ideas:

• Trade is a positive-sum game: both countries benefit.

• Gains from trade are similar to increases in TFP: trade increases aggregateconsumption opportunities.

• Trade creates winners and losers, but the winners win more than the loserslose. Trade affects the kind of jobs that are available, not the number ofjobs.


3The Production Function

Tools: Cobb-Douglas production function.

Key Words: Productivity (TFP); constant returns to scale, diminishingmarginal product, capital, labor.

• A production function relates output (real GDP) to inputs (capital andlabor). Ours have three essential properties: (i) more inputs lead to moreoutput; (ii) diminishing returns to capital and labor; (iii) constant returnsto scale.

• The Cobb-Douglas production function is a specific form that we’ll usethroughout.

• Total factor productivity (TFP) is the overall efficiency with which inputsare transformed into outputs.

We want to understand why some countries are richer than others, in thesense of having higher GDP per capita. Since rich means they producemore output, the question becomes where the output comes from. Herewe describe a tool for answering that question: a production function thatrelates the quantity of output produced to (i) the quantities of inputs and(ii) the efficiency or productivity with which they’re used. Doing this foran entire economy takes a leap of faith, but the reward is a quantitativesummary of the sources of aggregate economic performance.

3.1 The production function

Economic organizations transform inputs (factories, office buildings, ma-chines, labor with a variety of skills, intermediate inputs, and so on) into

45


outputs. Boeing, for example, owns factories, hires workers, buys electricityand avionics, and uses them to produce aircraft. American Express’s creditcard business uses computers, buildings, labor, and small amounts of plasticto produce payment services. Pfizer hires scientists, MBAs, and others todevelop, produce, and market drugs. McKinsey takes labor and informationtechnology to produce consulting services.

For an economy as a whole, we might think of all the labor and capital usedin the economy as producing real GDP, the total quantity of goods andservices. A production function is a mathematical relation between inputsand output that makes this idea concrete:

Y = AF (K,L),

where Y is output (real GDP), K is the quantity of physical capital (plantand equipment) used in production, L is the quantity of labor, and A is ameasure of the productivity of the economy. We call A total factor produc-tivity. More on each of these shortly.

The production function tells us how different amounts of capital and labormay be combined to produce output. The critical ingredient here is thefunction F . Among its properties are

1. More input leads to more output. In economic terms, the marginalproducts of capital and labor are positive. In mathematical terms, outputincreases in both K and L:

∂Y

∂K> 0,

∂Y

∂L> 0.

2. Diminishing marginal products of capital and labor. Increasesin capital and labor lead to increases in output, but they do so at adecreasing rate: The more labor we add, the less additional output weget. You can see this in Figure 3.1. For a given capital stock K, increasinglabor by an amount ∆ starting from L1 has a larger effect on output thanincreasing labor by the same amount starting from L2 > L1. That is:AF (K, L1 + ∆) − AF (K, L1) > AF (K, L2 + ∆) − AF (K, L2). Thiscondition translates into properties of the second derivatives:

∂2Y

∂K2< 0,

∂2Y

∂L2< 0. (3.1)

3. Constant returns to scale. This property says that if we (say) doubleall the inputs, the output doubles, too. More formally, if we multiply both

3. The Production Function 47

Figure 3.1: The production function.

-

6

L

Y

L1 L1 + ∆ L2 L2 + ∆

Y = AF (K, L)

inputs by the same number λ > 0, then we multiply output by the sameamount:

AF (λK, λL) = λAF (K,L). (3.2)

Thus, there is no inherent advantage or disadvantage of size.

These properties are more than we need for most purposes, but we mentionthem because they play a (sometimes hidden) role in the applications thatfollow.

Our favorite example of a production function is F (K,L) = KαL1−α, whichleads to

Y = AKαL1−α (3.3)

for a number (“parameter”) α between zero and one. Circle this equationso that you remember it! It’s referred to as the Cobb-Douglas version of theproduction function to commemorate two of the earliest people to use it.(Charles Cobb was a mathematician. Paul Douglas was an economist andlater a US senator.) Let’s verify that it satisfies the properties we suggested.First, the marginal product of capital and labor are

∂Y/∂K = αAKα−1L1−α = αY/K

∂Y/∂L = (1− α)AKαL−α = (1− α)Y/L.

Note that both are positive. Second, the marginal products are both de-creasing. We show this by differentiating the first derivatives to get second


derivatives:

∂2Y/∂K2 = α(α− 1)AKα−2L1−α

∂2Y/∂L2 = −α(1− α)AKαL−α−1.

Note that both are negative. Finally, the function exhibits constant returnsto scale. If we multiply both inputs by λ > 0, the result is

A(λK)α(λL)1−α = AλαKαλ1−αL1−α = λAKαL1−α,

as needed. We will typically use α = 1/3. If you’d like to know why, see the“Review questions” at the end of the chapter.

3.2 Capital input

The capital input (or capital stock) K is the total quantity of plant andequipment used in production. We value different kinds of capital (machines,office buildings, computers) at their base-year prices, just as we do with realGDP in the National Income and Product Accounts. It’s somewhat heroicto combine so many different kinds of capital into one number, but that’sthe kind of people we are.

Fine points:

• How does capital change over time? Typically, capital increases withinvestment (purchases of new plant and equipment) and decreases withdepreciation. Mathematically, we might write

Kt+1 = Kt − δtKt + It, (3.4)

where δt is the rate of depreciation between t and t+ 1. On average, thecapital stock depreciates about 6 percent a year, but this is an averageof depreciation rates for structures (which depreciate more slowly) andequipment (for example, computers, which depreciate more quickly). Inpractice, we use (3.4) to construct estimates of the capital stock frominvestment data.

Digression. Note that we’ve used a different timing convention than financial ac-

countants. Capital at time t is the amount available for production during the period.

We use the amount available at the start of the period, which in financial statements

would be the end of the previous period. Why do we do this? Because, otherwise,

current production would depend on last period’s capital stock, which seems a little

strange. Note, too, that for a period like a year, this is a moving target: The amount

of capital available in December is likely to be different from the amount available

in March. That’s not a big deal, because the capital stock is slow to change, so any

changes within a period are likely to be small relative to the total.


• Quality. In principle, we want to take into account changes over time inthe quality of capital. Computers, for example, are more productive thanthey were ten years ago, so a computer today should count as more capitalthan a computer ten years did. Ideally, this happens when we constructour real investment series: the national income and product accountantsconsider changes in quality when they divide investment into price andquantity components. In recent times, the effect of this has been a sharpdecrease in the price of investment goods, particularly equipment, so thata given dollar expenditure results in greater additions to capital than inthe past.

• Wars and natural disasters. Wars can have an impact on the capitalstock—natural disasters, too, although their impact is rarely as big. Ex-perts estimate that the German and Japanese capital stocks declined byabout 50 percent between the start and end of World War II. In moderntimes, the impact is almost always negligible. September 11 and Hurri-cane Katrina, for example, had enormous effects on New York City andNew Orleans, respectively, but the impact on the US capital stock wastiny in both cases.

• Does land count? The short answer: No. In principle, maybe it should,but in modern economies, land is far less important than plant and equip-ment. For very poor agricultural economies, land and livestock are im-portant inputs to production, but they’re not typically included in ourmeasures of the capital stock.

• Intangibles. Capital here consists solely of physical capital. We donot include “investments” in such things as research and development,patents, brands, and databases. These aren’t part of traditional measuresof capital yet, but there’s been some progress towards including them.

3.3 Labor input

The next component of our production function is labor. The first-orderapproximation is simply the number of people employed (L), which is anumber we can find for most countries. (It’s not as easy as you might thinkto measure employment, especially in countries with a large informal sector.)In some cases, we also include measures of the quality of labor (“humancapital” H) and hours worked (h). If we include both, our measure of laborinput becomes hHL.

The starting point for the labor input is, of course, the population. Pop-ulations of countries differ not only in quantity, but also in their age dis-tribution and its evolution. Right now, for example, China has a relatively


young population, but with a low birth rate, it is aging rapidly. The US hasa younger population than Europe or Japan, the result of a higher birth rate(more young people!) and a higher immigration rate (immigrants tend tobe young, too). These demographic issues are interesting in their own right.They play an important role in government policy—many countries havestate-supported pension and health-care systems, for example, so changesin the age distribution can have a significant impact on government budgets.They’re also a critical input in product decisions, telling you, for example,whether you should be selling diapers or walkers.

Our focus, however, is on the quantity and quality of labor. There’s noquestion that individuals differ in skill. Derek Jeter’s skills earn him $15ma year as a shortstop for the New York Yankees baseball team, but most ofus would be worth far less in the same job. American workers earn morethan Mexican and Chinese workers, in part because their skills are better.There are many skills we might want to measure. One that’s relatively easyto measure is the level of education of the workforce. In 2013, the averageKorean worker had 11.8 years of schooling, and the average Mexican workerhad 8.5 years. We know that individuals with more education have highersalaries, on average, so we might guess that Koreans have higher averageskills than Mexicans. We call this school-based difference in skill humancapital and take it into account by putting it into our production function:

Y = AF (K,HL),

where H is a measure of human capital.

There are two common measures we could use, both tied to the number ofyears of school S of the workforce. The first is to set human capital equalto average years of school:

H = S.

This seems to be a relatively good approximation for most purposes, butit leads to unreasonably large percentage increases in H at low levels ofschooling. For example, workers in India had an average level of schooling of1.7 years in 1960, so one additional year of school increases H by 59 percent.Another approach, based on a huge body of evidence, is to credit each yearof school with (say) a given percentage increase in skill. Mathematically, wemight say

H = exp(σS),

where σ is the extra value of a year of school. A good starting point isσ = 0.07, which means that every year of school increases human capital by7 percent.

A second refinement of our measure of labor input focuses on quantity: thenumber of hours worked. Curiously enough, there are substantial differences


in average hours worked across countries. If we use h to represent hoursworked, our state-of-the-art modified production function is

Y = = AF (K,hHL) = AKα(hHL)1−α. (3.5)

3.4 Productivity

The letter A in the production function plays a central role in this course.We refer to it as total factor productivity or TFP, but what is it? Wheredoes it come from?

The word productivity is commonly used to mean several different things.The most common measure of productivity is the ratio of output to la-bor input, which we’ll call the average product of labor . This is typicallywhat government agencies mean when they report productivity data. Itdiffers from the marginal product of labor for the same reason that averagecost differs from marginal cost. Total factor productivity , the letter A inthe production function, measures the overall efficiency of the economy intransforming inputs into outputs.

Mathematically, the three definitions are:

average product of labor = Y/L

marginal product of Labor = ∂Y /∂L

total factor productivity = Y/F (K,L).

For the Cobb-Douglas production function they are:

average product of labor = A (K/L)α

marginal product of Labor = (1− α)A (K/L)α

total factor productivity = A.

Holding A constant, the first two increase when we increase the ratio ofcapital to labor. Why? You can be more productive if you have (say)more equipment to work with. TFP is an attempt to measure productivityindependently of the amount of capital each worker has. That allows us totell whether the US is more prosperous than India because it has more andbetter capital (higher K) or uses the labor and capital it has more effectively(higher TFP A).

In practice, we measure total factor productivity as a residual: We measureA by taking a measure of output (real GDP Y ) and comparing it to measures


of capital and labor inputs. In the simplest case (without corrections tolabor), we solve

A = Y/(KαL1−α).

As a result, anything that leads the same inputs to produce more outputresults in higher TFP. What kinds of things might do this? One example isinnovation. If we invent the computer chip or a drug that cures cancer, theywill clearly increase measured productivity (or one would hope they would).But there are many other examples. Another example is security. If weestablish personal safety and security, then individuals can spend more timeworking productively, and less time worrying about being robbed or mur-dered. Another is competition. If the economic system reallocates resourcesfrom less-productive to more-productive firms, that will lead to an increasein country-wide productivity. Capital and labor-market laws and regula-tions play a clear role here. In short, anything that affects the allocation ofresources can have an impact on total factor productivity.

3.5 Marginal products

In competitive markets, labor and capital are paid their marginal products.We could show that, but for now would prefer to simply take it on faith.That, in turn, tells us where payments to labor and capital come from.

Consider payments to labor. Firms hire workers until the marginal productof an additional unit of labor equals its cost, the wage w. We’ll go into thisin more detail when we study labor markets, but for now note that this bitof logic can be represented mathematically by

w = MPL ≡ ∂Y /∂L,

where MPL means the marginal product of labor. With our basic Cobb-Douglas production function (3.3), this becomes

w = (1− α)AKαL−α = (1− α)A (K/L)α

= (1− α)Y/L.

We can now ask ourselves: What do we need to generate high wage rates?The answer: High total factor productivity and/or high capital-labor ratios.In words, workers are more productive, at the margin, if TFP is high and ifthey have more capital to work with.

Note that high wages are a good thing for an economy: they reflect (forexample) high productivity. Often, countries with high TFP also have highcapital per worker, so the two terms drive wages in the same direction. Itdoesn’t seem fair, but it happens because the same productivity that makesworkers valuable also raises the return on capital, as we see next.


The market return on capital (r, say) equals the marginal product of capital.In this case, there’s an additional adjustment for depreciation, so we have

r = MPK = αA (K/L)α−1 − δ = αY/K − δ.

The right-hand side here is the net marginal product of capital—net be-cause we have netted out depreciation. Without that term, we have thegross marginal product of capital, because our measure of output is gross ofdepreciation (the G in GDP).

In short, the productive value of labor and capital (ie, their marginal prod-ucts) depends in large part on total factor productivity. To understand this,it’s important that you be able to distinguish between total factor produc-tivity (the letter A in the production function) and the marginal productsof labor and capital.

Executive summary

1. A production function links output to inputs.

2. Inputs include physical capital (plant and equipment) and labor (possiblyadjusted for skill and hours worked).

3. Total Factor Productivity (TFP) is a measure of overall productive effi-ciency.

Review questions

1. Components of the production function. A small country invests a largefraction of GDP in a major infrastructure project, which later turns intoa “white elephant” (that is, it’s not used). How does this affect thecomponents of the production function?

Answer. The investment will raise the stock of capital K, but since it’snot used, we would expect no increase in output Y . We would, therefore,expect measured productivity to fall.

2. Computing TFP. Suppose an economy has the production function

Y = AK1/4L3/4.

If Y = 10, K = 15, and L = 5, what is total factor productivity A?

Answer. A = Y/(K1/4L3/4) = 1.520.


3. Diminishing returns. Suppose the production function is

Y = 2K1/4L3/4

and K = L = 1. How much output is produced? If we reduced L by 10percent, how much would K need to be increased to produce the sameoutput?

Answer. With K = L = 1, Y = 2. If L falls to 0.9, K = 1/0.93 = 1.372(a 37 percent increase in K). The reason for the difference between themagnitudes in the changes in K and L is the difference in their exponentsin the production function.

4. Human capital 1. Worker 1 has ten years of education, worker 2 has 15.How much more would you expect worker 2 to earn? Why?

Answer. If H = years of education, then one hour of worker 2’s time isequivalent to 1.5 (= 15/10) hours of worker 1’s time, so we’d expect herto be paid 50 percent more. A more complex answer is that skill mayincrease in a more complicated way with years of education, and thattypes of education may differ in their impact on earning power (an MBAmay be worth more in this sense than a PhD in cultural anthropology,however interesting the latter may be).

5. Human capital 2. Consider the augmented production function

Y = K1/3(HL)2/3.

If K = 10, H = 10, and L = 5, what is the average product of labor ?How much does the average product increase if H rises to 12?

Answer. Output is Y = 29.24 so Y/L = 5.85. If H rises to 12, Y/L =6.60.

6. Production function conditions. Conditions 2 and 3 [equations (3.1) and(3.2)] seem to contradict each other. One says increases in inputs havea declining impact on output, while the other says that proportionalincreases in capital and labor lead to the same proportional increase inoutput. What’s going on here?

Answer. This is a subtle issue, but the answer is that the conditions aredifferent. Condition 2 concerns increases in one input, holding constantthe other input . Condition 3 concerns increases in both inputs at thesame time. Different concepts, different properties.

7. One-third. Why does α = 1/3?

Answer. If we look at the income side of the National Income and ProductAccounts, about two-thirds is paid to labor and one-third to capital. We’ll


see later that firms will hire labor until its marginal product equals thewage. For our Cobb-Douglas production function,

w = MPL = (1− α)AKαL−α.

Total payments to labor are the product of the wage and labor:

wL = (1− α)AKαL1−α = (1− α)Y.

So we set 1− α = 2/3, as stated.


The methodology described in this chapter has been applied, with lots ofvariations, to countries, industries, and even firms. The biggest challenge inmost studies is coming up with capital stocks. We use the Penn World Tableand construct country-level capital stocks ourselves, which we can then useto compute productivity. If you’re interested, and can’t find it online, sendus an email.

Lots of other organizations do their own calculations. Two of the most usefulpublic sources are

• The Bureau of Labor Statistics. They report what they call “multifactorproductivity,” both levels and growth rates, for the US private businesssector and a number of industries:

http://www.bls.gov/bls/productivity.htm.

• The Conference Board. Their Total Economy Database includes growthrates of aggregate TFP for a number of countries:

http://www.conference-board.org/data/economydatabase/.

http://www.bls.gov/bls/productivity.htm

http://www.conference-board.org/data/economydatabase/


Symbols used in this chapter


Symbol Definition

Y Output (real GDP)A Total factor productivity (TFP)K Stock of physical capital (plant and equipment)L Quantity of labor (number of people employed)F (K,L) Production function of K and L∂F (K,L)/∂K Partial derivative of F (K,L) with respect to K∂F (K,L)/∂L Partial derivative of F (K,L) with respect to L∆ Infinitesimal numberK Given capital stockλ Constantα Exponent of K in Cobb-Douglas production function

(= capital share of income)δ Rate of depreciation of physical capitalI Investment (purchases of new plant and equipment)H human capitalh Hours workedhHL Volume of labor inputS Years of school of workforceσ Extra value of a year of schoolw Wager market return on capital (or rental cost of capital)

4The Solow Model

Tools: Capital accumulation dynamics; Cobb-Douglas production function.

Key Words: Investment; saving; depreciation; steady state; convergence.

Big Ideas:

• The Solow model connects saving and investment with economic growth.

• In the Solow model without productivity (TFP) growth, capital accu-mulation does not generate long-run growth. The reason is diminishingreturns to capital: the impact of additional capital declines the more youhave. As a result, differences in saving rates have only modest effects onoutput per worker and none at all on its long-run growth rate.

• TFP growth generates long-run growth in output per worker.

We see large differences in saving and investment rates across countries, with(for example) the US investing 20 percent of GDP, China 40 percent, andIndia 30 percent in recent years (ratios of real investment to real GDP fromthe Penn World Tables). How important are these differences to the growthrates of countries? The answer: not important at all. Why? Becausediminishing returns to capital means (in practice) that additional capitalgenerates smaller and smaller additions to output. This insight comes fromwork by Robert Solow, who received the 1987 Nobel Prize in economics forhis work. His model is also a useful tool for extrapolating current trendsand pointing out the critical inputs to any such exercise.

57


4.1 The model

Solow’s model has four relatively simple components. The first is our friendthe production function:

Yt = AtF (Kt, Lt) = AtKαt L

1−αt . (4.1)

Changes in output, therefore, come from changes in (total factor) productiv-ity, capital, and/or labor. Recall that one of the properties of this productionfunction is diminishing returns to capital — each additional unit of capitalleads to a smaller addition to output. This is the critical ingredient in whatfollows. The second component is a link between investment and saving.You’ll recall that the flow identity, S = I+ NX , linked saving to investmentand net exports. Solow ruled out the last one (we can put it back later ifwe like), giving us

St = It.

Lurking behind the scenes here is the expenditure identity, Y = C + I inthis case.

The third component is a description of saving behavior: people save aconstant fraction s of their income,

St = sYt,

where the saving rate s is a number between zero and one. This is a littlesimplistic — you might expect saving to depend on the rate of return and/orexpectations of future income — but there is a lot to be said for simplicity.For our purposes, s is really the investment rate (the ratio of investment toGDP), but since saving and investment are the same here, we can call it thesaving rate. Finally, the capital stock depreciates at a constant rate δ, sothat

Kt+1 = (1− δ)Kt + It, (4.2)

where the depreciation rate δ is a number between zero and one.

The model consists of these four equations. This seems kind of simple for aNobel Prize, but they really are good equations. Now let’s see where theylead.

4.2 Capital dynamics

Let’s think about how the model behaves if the labor input L and productiv-ity A are constant. Analysis of the model in this case consists of describing

4. The Solow Model 59

Table 4.1: Output dynamics in the Solow model.

Date t Capital Stock K Output Y

0 250.0 135.71 252.1 136.12 254.2 136.53 256.0 136.84 257.8 137.15 259.4 137.46 261.0 137.77 262.4 137.98 263.8 138.29 265.0 138.4

10 266.2 138.6

how the capital stock evolves through time. Other variables follow fromtheir relations to the capital stock. We can find output from the productionfunction, saving (= investment) from output, and consumption (should weneed it) from the expenditure identity (C = Y − I).

The key step is to describe how the capital stock changes from one periodto the next. To do that, we add time subscripts to the equations that don’thave them already. Then, with a little work, we see that the capital stockbehaves like this:

Kt+1 = (1− δ)Kt + It

= (1− δ)Kt + St

= (1− δ)Kt + sYt

= (1− δ)Kt + sAKαt L

1−α. (4.3)

Note that each step follows from one of the components of the model. Theresult is a formula for computing Kt+1 from Kt and some other stuff. If wehave numerical values for the parameters (A,α, s, δ), we can do the compu-tations in a spreadsheet or other program and see how K moves throughtime.

Example. A numerical example will show you how this works. Let L = 100,A = 1, s = 0.2, δ = 0.1, and α = 1/3. (We’ll use the same parametersthroughout.) If the initial capital stock is 250, we can compute future valuesof the capital stock by applying equation (4.3) repeatedly. We then computeoutput from the capital stock using the production function. The results forthis case are summarized in Table 4.1. [Suggestion: Try to reproduce a fewperiods of the table to make sure you understand how it works. If you get


stuck, read the last two pages again. The trick is to set up formulas that tieeach period to the previous one.]

You can see in the table that capital and output both increase over time.Will they increase forever? The answer is no, but it takes a little workto show. (Alternatively, you could extend the simulation and see whathappens.) This is an important conclusion, because it tells us saving andcapital formation can’t be the reason (in this model, anyway) that somecountries grow faster than others. More on this soon.

The dynamics of the capital stock reflect a balance of two factors: (i) savingtends to increase the capital stock by financing new investment and (ii) de-preciation tends to reduce it. A modest change to equation (4.3) makes thisclear:

∆Kt+1 ≡ Kt+1 −Kt = sAKαt L

1−α − δKt. (4.4)

(The equal sign with three lines means that the equation defines the expres-sion that comes before it, in this case ∆Kt+1.) You can see that the changeis zero (the capital stock doesn’t change) when

Kss =

(sA

δ

)1/(1−α)

L,

where Kss is the “steady-state” capital stock. This is a little complicated,but remember: it’s just a formula. In our example, Kss = 282.8, so we havea ways to go before the model reaches its steady state.

What happens if we are above or below Kss? You can get a sense of thedynamics from Figure 4.1. The top line is output, which is related to thecapital stock through the production function. The next line is saving, aconstant fraction of output and the first expression on the right side of equa-tion (4.4): sAKαL1−α. The third line is depreciation, a constant fraction δof the capital stock and the second object on the right side of equation (4.4):δK. Diminishing returns to capital gives the saving line its curvature. Itleads to higher saving than depreciation at low values of the capital stock, sothe capital stock is increasing. Similarly, saving is lower than depreciation athigh values of the capital stock, so the capital stock falls. The crossing pointis Kss, where saving is just enough to make up for depreciation, leaving thecapital stock unchanged.

4.3 Convergence

The central feature of the model is what we call the convergence property:If countries have the same parameters, they will eventually converge to the


Figure 4.1: The Solow model.

Output

Savings

Depreciation050

100

150

200

0 100 200 300 400Capital

same level of output per worker. We haven’t quite shown this yet, but theonly thing missing is the “per worker” qualification.

Consider, then, a version of the model in per-worker terms. The first stepis to divide both sides of (4.3) by L. If k ≡ K/L is capital per worker (orthe capital-labor ratio), the equation becomes

kt+1 = (1− δ)kt + sAkαt

or

∆kt+1 ≡ kt+1 − kt = sAkαt − δkt. (4.5)

You’ll note a resemblance to equation (4.4).

Figure 4.2 illustrates the model’s dynamics. It’s based on the same param-eter values as our earlier example: A = 1, s = 0.2, δ = 0.1, and α = 1/3.The line marked “saving per worker” is the first expression on the rightside of equation (4.5): sAkα. The line marked “depreciation per worker”is the second expression on the right side of equation (4.5): δk. For smallvalues of k, saving per worker is greater than depreciation per worker, so kincreases. For large values of k, saving per worker is less than depreciationper worker, so k decreases. The two lines cross at the steady state, wherethe capital-labor ratio is constant. We can find the steady-state value of kfrom equation (4.5) by setting ∆kt+1 = 0. This leads to

kss =

(sA

δ

)1/(1−α)

,


Figure 4.2: The impact of the saving rate in the Solow model.

Higher savings per worker

Savings per worker

Depreciation per worker

0.0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5Capital per worker

a minor variant of our earlier expression for the steady-state capital stock.

We have shown that the capital-labor ratio eventually converges to its steady-state value. What about output per worker? The production function inper worker form is Y/L = Akα, so steady-state output per worker dependson steady-state capital per worker:

(Y/L)ss = Akαss = A

(sA

δ

)α/(1−α)= A1/(1−α)

(sδ

)α/(1−α). (4.6)

Similarly, the steady-state capital-output ratio is

(K/Y )ss =(sδ

).

The algebra isn’t pretty, but it tells us how the steady state depends on thevarious parameters. The last equation tells us, for example, that countrieswith higher saving rates also have higher steady-state capital-output ratios— that is more saving leads to more capital. Equally important, the exis-tence of a steady state tells us that if two countries have the same parametervalues, they will converge to the same output per worker. We refer to this asthe convergence property. In this model, any long-term differences betweencountries must come from differences in their parameters.


4.4 Impact of saving and investment

We can return to the question we began with: What is the impact of savingand investment rates on growth and income? The long-run impact of savingon growth is zero; the steady-state growth rate is zero, regardless of thesaving rate. But there is an effect of saving on steady-state output perworker.

Consider our example. From equation (4.6), we see that steady-state out-put per worker is 1.4142. What if we increase the saving rate s from 20percent to 25 percent? Then, steady-state output rises to 1.5811, an 11percent increase. This isn’t irrelevant, but it’s a relatively modest increasefor a substantial increase in saving. It clearly does not explain much of theenormous differences in GDP per capita that we see around the world.

We can see the same thing in Figure 4.2. The line marked “saving perworker” is based on a saving rate of s = 0.20, or 20 percent. If we raise thesaving rate to 25 percent, the saving line shifts up, as shown by the dashedline marked “higher saving per worker.” Why? Because sAkα is higherat every value of k. With this new line, the steady-state value of capitalper worker (where the saving line crosses the depreciation line) is higher, asshown.

4.5 Growth

If saving doesn’t generate growth, what does? We add growth in the laborforce and (critically) growth in total factor productivity with two goals inmind. The first goal is to account for the growth rate of output, showinghow it depends on the growth rates of our two inputs. The second is to showthat the economy approaches what we call a balanced growth path in whichoutput and capital grow at the same rate. As before, the capital-outputratio approaches a constant, the features of which we can easily summarize.We do this with a striking example in mind: We know that China investsan astounding 40 percent of its GDP. Is this too much? A hint is thatcapital intensity (measured by the capital-output ratio) depends not onlyon the investment rate (which tells us how much new capital is added), butalso on the growth rate (how fast the denominator is changing). A fast-growing economy needs a high investment rate simply to maintain a givencapital-output ratio.

The new inputs into our analysis are growth in the labor force and pro-ductivity. Let us say, to be concrete, that labor and productivity grow at


constant rates:

Lt+1 = (1 + gl)Lt

At+1 = (1 + ga)At.

How fast do output and capital grow? Let’s guess that output and capitalgrow at the same rate gy, to be determined. (Why? Because we’re goodguessers.) From the production function, we then know that

(1 + gy) = Yt+1/Yt

= (At+1/At)(Kt+1/Kt)α(Lt+1/Lt)

1−α

= (1 + ga)(1 + gy)α(1 + gl)1−α.

The growth rate, is therefore,

(1 + gy) = (1 + ga)1/(1−α)(1 + gl).

Just a formula, but it says that output growth is tied to the growth ratesof productivity and labor. The saving rate does not affect this growth rate.Similarly, the growth rate in output per worker is

(1 + gy)/(1 + gl) = (1 + ga)1/(1−α),

which depends only on productivity growth. If α is positive, the growthrate of output per worker is higher than the growth rate of productivity,because the exponent 1/(1 − α) is greater than one. In words, the directimpact of productivity on output is magnified by the growth in the stockof capital; see the production function (4.1). This ties in with a remark wemade earlier: That capital accumulation tends to reinforce the impact ofproductivity growth. Countries with high productivity also have a lot ofcapital.

What about capital — do countries with higher saving rates have morecapital, relative to the size of their economies? Consider, again, a steadystate in which capital and output grow at the same rate gy. Then Kt+1 =(1 + gy)Kt and equation (4.3) becomes

Kt+1 = (1− δ)Kt + sYt

(1 + gy)(Kt/Yt) = (1− δ)(Kt/Yt) + s.

Solving for K/Y gives us the steady-state capital-output ratio:

(K/Y )ss =

(s

δ + gy

).

To return to our goal of understanding the sources of capital intensity, notethe impact of growth on the steady-state capital-output ratio. For a given


saving/investment rate s, countries with higher growth gy will have relativelyless capital per unit of output. Why? Because when output is growingquickly, you need to invest a lot to keep capital growing at the same rate.

Example. Here are some numbers based loosely on the US: gl = 0.005(0.5%), ga = 0.01 (1%), s = 0.15, and δ = 0.06. What is the growth rate ofoutput? The steady-state capital-output ratio? The growth rate satisfies

1 + gy = (1 + ga)1/(1−α)(1 + gl) = 1.015× 1.005 = 1.0201.

Here, we’ve used α = 1/3, as usual. Using the same parameters as ourearlier examples, the steady-state capital-output ratio is

1.872 =0.15

0.06 + 0.020.

Now consider numbers based on China. We keep gl = 0.005 and δ = 0.06,but change the others to ga = 0.04 and s = 0.40. The growth rate is nowgy = 0.0659 and the capital-output ratio is 3.17. Note the moderate increase,despite the near tripling of the saving/investment rate. Is China investingtoo much? Perhaps not. Their capital-output ratio (by this calculation) isnot much different from that of the US, so the 40% investment rate isn’tdelivering excessive capital intensity by this measure. They need to investa lot simply to keep up with the growth of their economy.

Executive summary

1. Solow’s model bases growth on saving and investment.

2. Saving affects steady-state GDP per worker, but not its growth rate. Inthis sense and others, saving is secondary to long-term economic perfor-mance.

3. Fast-growing countries must invest more to maintain the same capital-output ratio.

Review questions

1. The basics. Suppose A = L = K = 1, α = 1/3, δ = 0.06, and s = 0.12.

(a) What is output Y ?

(b) What are saving S and investment I?

(c) What is next period’s capital stock?


Answer.

(a) Y = AK1/3L2/3 = 1.

(b) S = I = sY = 0.12.

(c) Put t’s on everything so far. Then Kt+1 = (1 − δ)Kt + I = 0.94 +0.12 = 1.06.

2. Example, continued. For the numerical example in the text:

(a) Suppose that the economy starts with the steady-state capital stock.What are the steady-state levels of output, investment, and con-sumption?

(b) If 25 percent of the capital stock is destroyed in a war, how longdoes it take the economy to eliminate half the fall in output?

Answer.

(a) The steady-state capital stock is (as we’ve seen) Kss = 282.8. Usingthis value, the production function tells us that output is 141.4.Investment equals the depreciation of the capital stock, 28.3. We canfind consumption in two ways. The first is through the expenditureidentity: Y = C + I. We know Y and I, so C is 113.1. Thesecond is through the flow identity. Saving is fraction s of output,so consumption is fraction 1− s, 0.8× 141.4 = 113.1.

(b) This requires a simulation. Let the capital stock fall to 212.1, 75percent of its steady-state value. Then, output is 128.5, 90.9 percentof its steady-state value. We recover half the fall if output rises to135.0. If we simulate the model, we see that it reaches 135.1 in 10periods (years).

3. Government. We’ve ignored government so far. Suppose, instead, thatthe government purchases goods and services equal to a constant fractionof GDP (say, G = dY for some fraction d) and collects taxes equal to thesame fraction of output. Individuals have after-tax income of (1 − d)Yand save a fraction s of it. With these changes, how would the analysisof the basic Solow model change?

Answer. The critical ingredient here is the fraction of output allocatedto investment. Investment here is I = S = s(1 − d)Y . Effectively, dreduces the saving rate from s to s(1− d) and takes resources away frominvestment. If the government invests, we’d have to include that, butwe’d also have to decide how useful the investment was (does it countthe same as other investment?).


This material is covered in many macroeconomics textbooks. Our favoritesare


• Tyler Cowen and Alex Tabarrok, Modern Principles: Macroeconomics, ch7.

• N. Gregory Mankiw, Macroeconomics (6th edition), chs 7-8.

Any editions will do, but the chapter numbers may vary.

Goldman Sachs has used the Solow model (and some heroic assumptionsabout fundamentals) to forecast the importance of the BRICs (Brazil, Rus-sia, India, and China) to the world economy in 50 years. See “Dreamingwith BRICs.” It’s a good example of how assumptions about productivity,population growth, and education can be used to generate plausible sce-narios for the sizes of economies in the distant future. (The equations ontheir page 18 should look familiar.) This doesn’t make forecasting any lesshazardous, but it tells you what the critical inputs are. The key one here,of course, is productivity growth.



Symbol Definition

Y Output (real GDP)A Total factor productivity (TFP)K Stock of physical capital (plant and equipment)L Quantity of labor (number of people employed)F (K,L) Function of inputs K and L in production functionα Exponent of K in Cobb-Douglas production function

(= capital share of income)S SavingI InvestmentC Consumptions Saving rate as a percent of income Yδ Rate of depreciation of physical capital∆K Change of K (= Kt+1 −Kt)Kss Steady-state capital stock(K/Y )ss Steady-state capital-output ratiok Capital per worker, or capital-labor ratio (= K/L)gy Discretely-compounded growth rate of Ygl Discretely-compounded growth rate of Lga Discretely-compounded growth rate of Ad Government purchases as a share of output (G/Y )

http://www.goldmansachs.com/korea/ideas/brics/99-dreaming.pdf

http://www.goldmansachs.com/korea/ideas/brics/99-dreaming.pdf


5Sources of Economic Growth

Tools: Cobb-Douglas production function; level and growth accounting;continuously-compounded growth rates.

Big Ideas:

• Level and growth accounting allow us to quantify the sources of growth:the contributions of capital, labor, and total factor productivity (TFP) togrowth in real GDP.

• TFP accounts for most of the cross-country differences in output perworker and in differences in the growth rate of output per worker.

If saving rates aren’t responsible for the enormous differences we see in livingstandards, what is? The answer is productivity, but our purpose here is todevelop a tool that will give us the answer, whatever it might be. Ouringredients are data (always a good thing) and a little bit of theory (theproduction function). The combination allows us to attribute differencesin output and its growth rate to differences in inputs (capital and labor)and total factor productivity (everything else). The answer, as noted, ismostly productivity: Rich countries are rich because they’re productive,and countries that are growing quickly typically have rapid productivitygrowth, as well. Robert Solow gets credit for this line of thought, too.

5.1 Cross-country differences in output per worker

The production function gives us some insight into cross-country differencesin GDP per worker. You’ll recall that the production function connects

69


an economy’s output (real GDP) to the quantity of inputs used in produc-tion (capital and labor) and the efficiency with which those inputs are used(productivity). In equation form:

Y = AF (K,L) = AKαL1−α, (5.1)

where (as before) Y is real GDP or output, A is total factor productivity(TFP), K is the capital stock, and L is the quantity of labor (typicallyemployment). More commonly, we divide both sides by L and express outputper worker as

Y/L = A(K/L)α, (5.2)

so that output per worker depends on total factor productivity (A) andcapital per worker (K/L). For most countries, we have reasonably gooddata for GDP, employment, and the capital stock, and productivity can befound as a residual:

A = Y/(KαL1−α). (5.3)

We’ll continue to use α = 1/3, so there is nothing about equations (5.1) and(5.2) that we don’t know. In this sense, the production function is no longeran abstract idea, but a practical tool of analysis.

Table 5.1: Data for Mexico and the US.

Employment Education Capital GDP

Mexico 46.94 7.61 4,278 1,293US 155.45 12.27 42,238 12,619

Aggregate data for 2009 (education for 2007). Employment isexpressed in millions, education in years, and capital and GDP inbillions of 2005 US dollars.

The production function allows us to make explicit comparisons across coun-tries. If we apply equation (5.2) to two countries and take the ratio, we get

(Y/L)1(Y/L)2

=

[A1

A2

] [(K/L)1(K/L)2

]α, (5.4)

where the subscripts 1 and 2 refer to the two countries. The ratio of outputper worker is, thus, attributed to some combination of the ratios of TFPand capital per worker. Exercises based on (5.4) are referred to as levelcomparisons. If we have data, we can say which of these factors is mostimportant.

If we did this in logarithms, the components would add rather than multi-ply. As a result, the contribution of each component can be expressed as a

5. Sources of Economic Growth 71

fraction the total. We were tempted to do this, but worried it would undulytry your patience.

Example (Mexico and US). You occasionally hear people in the USsay that Mexican workers are paid so much less that they pose a threat toAmerican jobs. (In Mexico, you hear the same thing about Chinese workers.)We can’t address that issue (yet) but we can say something about the sourceof differences in output per worker, which is closely related to differences inwages. The data in Table 5.1 imply that output per worker is 2.95 timeshigher in the US, but why? We’ll use the data in Table 5.1 to come up withan answer.

Let’s start with TFP. For Mexico, the data in the table imply that

AM = 1293/[42781/346.942/3] = 6.12.

A similar calculation for the US gives us AUS = 12.53. Thus, TFP is 2.05(= 12.53/6.12) times higher in the US. Similarly, the capital-labor ratio is2.98 times higher in the US. The impact on output per worker is summarizedby

(Y/L)US(Y/L)M

=AUSAM

[(K/L)US(K/L)M

]1/3= (2.05)(2.98)1/3

= (2.05)(1.44) = 2.95.

It seems, therefore, that both TFP and capital per worker play a role inaccounting for the 2.95-to-1 ratio of US to Mexican output per worker. Sothe reason why output per worker is higher in the US is a combination ofhigher productivity and higher capital per worker.

This is your chance for speculation: Why do you think the capital-laborratio is lower in Mexico? Why do you think productivity is lower?

5.2 Cross-country differences in growth rates

Our next task is to apply similar methods to account for cross-country dif-ferences in growth rates rather than levels.

Warning, growth rates ahead: Before you continue, you might want togo back and review continuously-compounded growth rates in the Mathe-matics Review, Chapter 1.


As before, the starting point is the production function. If we take thenatural logarithm of both sides of the production function (5.1), we findthat

lnYt = lnAt + α lnKt + (1− α) lnLt

for any date t. This follows from two properties of logarithms: ln(xy) =lnx+ ln y and lnxa = a lnx. If we take the difference between two adjacentperiods t and t− 1 we get

lnYt−lnYt−1 = (lnAt−lnAt−1)+α(lnKt−lnKt−1)+(1−α)(lnLt−lnLt−1).

Notice that each of the components should be recognizable as continuously-compounded growth rates discussed in the growth-rate discussion.

If we consider differences over n periods, we can divide each term by thenumber of periods to get(

lnYt − lnYt−nn

)=

(lnAt − lnAt−n

n

)+ α

(lnKt − lnKt−n

n

)+ (1− α)

(lnLt − lnLt−n

n

).

Notice that we have expressed the average, continuously-compounded growthrate of GDP into the average, continuously-compounded growth rate of eachcomponent of the production function (i.e., TFP, capital, and labor). Us-ing our notation convention that continuously-compounded growth rates arerepresented by γ, we can express the formula above more succinctly as

γY = γA + αγK + (1− α)γL. (5.5)

In words, this equation says that the growth rate of output can be attributedto growth in TFP, capital, and labor. Moreover, the terms add up becauseof our use of logarithms and continuously compounded growth rates. Addi-tivity is nice, as it allows us to make statements about the contributions ofeach component to the growth of GDP.

As with levels, we can do the same for the growth rate of output per worker:

γY/L = γY − γL= γA + α(γK − γL)

= γA + αγK/L. (5.6)

Exercises based on (5.5) and (5.6) are referred to as growth accounting , whichallows us to make statements about the contributions of each component inaccounting for the growth of GDP (5.5) or GDP per worker (5.6).


Both versions of growth accounting give us some insight into the sources ofeconomic growth, as the example below shows.

Example (Chile between 1965 and 2009). GDP increased by almost afactor of five between 1965 and 2009. Can we say why? The relevant dataare reported in Table 5.2.

Table 5.2: Chilean aggregate data for 1965 and 2009.


1965 2.71 4.77 65.63 33.622009 7.52 7.97 819.81 199.2

The first step is to compute growth rates. Over this period, the averageannual growth rate of real GDP was

γY =lnY2009 − lnY1965

44= (5.29− 3.52)/44 = 0.0404,

or 4.04 percent. Using the same method, we find that the growth rates ofthe other variables we need are γK = 5.74 percent and γL = 2.32 percent.The growth rate of total factor productivity is the residual in equation (5.5):

γA = γY − [αγK + (1− α)γL] = 0.58%.

(You could also compute A for each period and calculate the growth ratedirectly.) So why did output grow? Our numbers indicate that of the4.04 percent growth in output, 0.58 percent was due to TFP; 1.91 percent[= 5.74× 1

3 ] was due to increases in capital; and 1.55 percent [= 2.32×(2/3)]was due to increases in employment.

What about output per worker? That seems to be the more interestingcomparison, because it’s closer to an average living standard. The growthrate of output per worker is γY/L = 1.72 percent. Its components are

γY/L = γA + αγK/L

1.72 = 0.58 + (1/3)3.42.

In this case, most of the growth in output per worker came from capital perworker, rather than TFP.

5.3 Extensions

We will sometimes use modifications of these tools. Two of the more commonones are based on (i) more-refined measures of labor and/or (ii) GDP per


capita rather than GDP per worker. The logic is the same as before, but wegain an extra term or two.

Labor measures. Consider a measure of labor that includes adjustmentsfor hours worked h and human capital H. If the labor input is hHL (withL the number of people employed), the production function becomes

Y = AF (K,hHL) = AKα(hHL)1−α. (5.7)

How does this change our analysis of levels and growth rates? In a levelcomparison, this leads to

Y1Y2

=

[A1

A2

] [K1

K2

]α [L1

L2

]1−α [h1h2

]1−α [H1

H2

]1−α.

The subscripts 1 and 2 again represent countries. You can derive furthermodifications for output per worker (Y/L) and output per hour worked(Y/hL). In a growth-rate analysis, the augmented production function (5.7)leads to

γY = γA + αγK + (1− α)(γh + γH + γL)

for output and

γY/L = γA + αγK/L + (1− α)(γh + γH)

γY/hL = γA + αγK/hL + (1− α)γH

for output per worker and output per hour, respectively. If this soundscomplicated, remember that the choice of tool depends on the question we’retrying to answer.

We have some choices when it comes to measuring human capital capital.One simple choice is to equate human capital capital with years of school:H = S if we want to give it mathematical form. A more sophisticated choiceis to give education a rate of return, so that

H = exp(σS), (5.8)

where σ is kind of a rate of return on school, as each year raises humancapital capital proportionately. Estimates of σ are in the range of 0.07, sothat each year of school raises human capital capital by about 7 percent.

Per capita GDP. The analysis above concerned GDP per worker (ratherthan per capita). How can we adapt our analysis to account for GDP percapita? Here’s a trick: start with equation (5.2) and multiply both sides bythe ratio of employment to population:

Y/POP = (L/POP)(Y/L) = (L/POP)A(K/L)α.


In a level comparison, this gives us an extra term: the ratio of L/POP acrosscountries. In growth rates, we’d add an extra term for the growth rate ofthe employment ratio:

γY/POP = γL/POP + γA + αγK/L.

And if you want to get fancy, you can add hours and human-capital terms,as we did above.

Example (Mexico and US, revisited). How does our analysis of theUS and Mexico change if we incorporate differences in human capital? Weset human capital H equal to years of school and redo our earlier analysis.TFP is now

AM = 1293/[42781/3(7.61× 46.94)2/3] = 1.58

for Mexico and AUS = 2.36 for the US. Note that the ratio has fallen from2.05 to 1.49. Why? Because part of the previous difference now shows upin human capital. [Reminder: A is a residual, so any change in the analysischanges our measure of it.] We now attribute some of the difference inoutput per worker to a difference in education:

(Y/L)US(Y/L)M

=AUSAM

[(K/L)US(K/L)M

]1/3 [HUS

HM

]2/3= (1.49)(2.98)1/3(1.61)2/3

= (1.49)(1.44)(1.38) = 2.95.

It appears that more than half of our earlier difference in TFP stems fromdifferences in education. We amend our previous analysis to add: A sub-stantial part of the difference between output per worker in the US andMexico stems from differences in education.

An alternative is to measure human capital using our rate-of-return formula,equation (5.8). If we do this, the ratio of human capital is 1.39, which isless than we had before. This choice makes an even bigger difference withcountries like India, which have low average education. If years of schoolgo from two to three, is that a 50-percent increase in human capital or aseven-percent increase? You be the judge. Of course, it may depend onwhat they learn in school, too.

Executive summary

1. Recall that a production function links output to inputs and productivity.


2. Therefore, differences in output and growth rates across countries stemfrom differences in the levels and growth rates of inputs and productivity(TFP).

3. Level accounting and growth accounting allows us to quantify the differ-ences in output and growth arising from differences in inputs and totalfactor productivity.

Review questions

1. Growth rates. Take the following data:

Output Y Employment L

1950 10 22000 50 3

(a) What are the average annual continuously-compounded growth ratesof Y and L?

(b) What is the analogous growth rate of Y/L?

Answer.

(a) The growth rate of output is

γY = [ln(50)− ln(10)]/(2000− 1950) = 0.0322,

or 3.22% per year. A similar calculation gives us γL = 0.0081 =0.81% per year.

(b) We can do this two ways. The easiest is

γY/L = γY − γL = 0.0241.

You can also compute it by dividing Y by L and applying the samemethod we used in (a).

2. France and the UK. In 2007, the data were:


France 29.51 8.48 6,478 1,986UK 31.79 9.88 5,243 2,070

Which country had higher output per worker? Why? You should assumethat human capital is equal to years of school.


Answer. Ratios were as follows:((Y/L)F

(Y/L)UK

)=

(AFAUK

)((K/L)F

(K/L)UK

)1/3(HF

HUK

)2/3

1.03 = (1.04)(1.33)1/3(0.86)2/3.

That is, France had slightly higher TFP and more capital per worker,but a lower level of education than the UK.

3. US and Japan. Explain why output grew faster in Japan between 1970and 1985. Data:

United States Japan

1970 1985 Growth 1970 1985 Growth

GDP 2083 3103 2.66 620 1253 4.69Capital 8535 13039 2.83 1287 3967 7.50Labor 78.6 104.2 1.88 35.4 45.1 1.61

Employment is measured in millions of workers, GDP and capital inbillions of 1980 US dollars. Growth rates are continuously-compoundedaverage annual percentages.

Answer. In levels (as opposed to growth rates), we see that the US hadmuch greater output per worker in 1970: 26.5 (thousand 1980 dollars perworker) vs 17.5. Where did this differential come from? One differenceis that American workers in 1970 had three times more capital to workwith: K/L was 108.6 in the US, 36.4 in Japan. If we use our productionfunction, we find that total factor productivity A was also slightly higherin the US in 1970: 5.55 v. 5.29. Thus, the major difference between thecountries in 1970 appears to have been in the amount of capital: Ameri-can workers had more capital and, therefore, produced more output, onaverage.

By 1985, much of the difference had disappeared. For the US, the outputgrowth rate of 2.66 percent per year can be divided into 0.94 percent dueto capital and 1.26 percent due to employment growth. That leaves 0.47percent for growth in total factor productivity. For Japan, the numbersare 2.48 percent for capital, 1.08 percent for labor, and 1.13 percent forproductivity. Evidently, the largest difference between the two countrieswas in the rate of capital formation: Japan’s capital stock grew muchfaster, raising its capital-labor ratio from 36.4 in 1970 to 88.0 in 1985.



Our calculations are based on various editions of the Penn World Table,

http://www.rug.nl/research/ggdc/data/penn-world-table,

which includes data on GDP per worker and related variables constructedon a consistent basis for most countries in the world. We typically post aspreadsheet of the latest version for our classes, but this is the source.

The tools of growth accounting are widely used by industry analysts. Someof the most interesting applications have been done by McKinsey, whosestudies have connected cross-country differences in TFP to government reg-ulation, management practices, and the competitive environment. Some ofthis work is summarized in William Lewis’s The Power of Productivity (Uni-versity of Chicago Press, 2004). Other examples are available on McKinsey’sweb site; search “mckinsey productivity.”



Symbol Definition

Y Output (real GDP)POP PopulationA Total factor productivity (TFP)K Stock of physical capital (plant and equipment)L Quantity of labor (number of people employed)F (K,L) Function of inputs K and L in production functionα Exponent of K in Cobb-Douglas production function

(= capital share of income)γx continuously-compounded growth rate of variable xgx Discretely-compounded growth rate of variable xln Natural logarithm (inverse operation of exp)exp Exponential function (inverse operation of ln)h Hours worked per workerH human capitalσ Value of an extra year of schooling

(= rate of return on schooling)Y/POP Output per capitaL/POP Ratio of employment to population

http://www.rug.nl/research/ggdc/data/penn-world-table

http://www.rug.nl/research/ggdc/data/penn-world-table

http://www.mckinsey.com/insights/mgi/research/productivity_competitiveness_and_growth

http://www.mckinsey.com/insights/mgi/research/productivity_competitiveness_and_growth

6Institutions and Policies

Key Words: Institutions; governance; time consistency; property rights;markets.

Big Ideas:

• Cross-country differences in productivity (TFP) are connected to differ-ences in institutions that shape productivity and policy.

• Good institutions include good governance; time consistency; rule of law;property rights; open and competitive markets.

The enormous international differences in GDP per person reflect, in largepart, enormous differences in productivity. But where do these differencesin productivity come from? It’s tempting to attribute them to the abil-ity and dedication of the people who live there, but (on second thought)there are smart, dedicated people everywhere. We now believe that pro-ductivity reflects the quality of local institutions and policies. Stated moreconcretely: it’s not Steve Jobs who makes an economy productive; it’s theinstitutions and policies that allow and encourage someone like Jobs to oper-ate effectively. Some countries have environments that encourage productiveactivity, and others do not. What’s striking is not that this is true, but howbig a difference it seems to make.

6.1 Good institutions

So what do we mean by good institutions? The world’s a complicated place,and it doesn’t come with any simple recipes. But countries with good eco-nomic performance share some features. We would say good institutions

79


are social mechanisms that facilitate good economic performance. Here’s ashort list.

Good governance. It’s essential that the government be strong enoughto guarantee the security and safety of the country and people, but not sostrong that those in power abuse others for their own benefit. It’s a delicatebalance, but most productive economies have both strong governments andclear limits to the government’s power.

Time consistency. Policy consistency over time reduces uncertainty andsupports economic growth. Institutions that allow governments to commitcredibly to good long-run policies (low inflation, fiscal prudence, etc.) helpreduce risks and allow businesses to plan with confidence.

If governments can easily renege on promises (say, to keep inflation andtaxes low) when it suits them, economic performance suffers. Finn Kydlandand Edward Prescott shared the 2004 Nobel prize partly for their analysisof this “time consistency” problem, which arises not just in economics butin many walks of life, from child-rearing to diplomacy, to military strategy.

In formal research, the lack of time consistency is known as the “dynamic in-consistency of intertemporal plans,” which arises when a future policymakeris likely to be motivated to break a current policy promise. Institutions andpractices that help governments pre-commit to future policies in a credi-ble way — such as the announcement of inflation targets by independentcentral banks or the constitutional prioritization of debt payments by stategovernments — help overcome the time-consistency problem.

Such pre-commitments typically involve the introduction of rules that limitpolicy discretion. You might think that allowing future policymakers com-plete discretion would result in the best possible policies. However, in thesenotes you will find numerous examples in which the ability to pre-commitresults in better economic outcomes (such as keeping inflation low or fos-tering greater investment). The reason is that a commitment to prudentpolicies has a favorable influence on the expectations and behavior of house-holds and businesses today. When economists incorporate the analysis oftime consistency into their assessment of various policy approaches, the age-old choice between policy rules and policy discretion usually tips in favor ofrules.

Rule of law. It’s also important that the legal system enforce the law: thatthe police and judiciary are honest and enforce the laws of the land.

Property rights. We sometimes take this for granted, but the laws shouldbe clear about who owns what. Without that, effective economic activity is

6. Institutions and Policies 81

impossible. How can you sell something you don’t own? Imaginative peoplemay be able to do just that, but it’s not a sound basis for a productiveeconomy. How can you get a mortgage if you can’t establish that you ownreal estate? Why would anyone lend on those terms?

Open and competitive markets. You often hear about “free markets,”but what seems to work best are honest, open, flexible, competitive marketsfor products as well as capital and labor. That’s different from what youmight term business-friendly governments, those who protect sellers fromcompetition or fraud. The idea is not to protect producers, but to allowthem to compete honestly.

We’ll give examples of each in class, but you might try to think of your own.

6.2 Institutions or policies?

Institutions bring to mind the difference between North and South Korea.The two countries have the same culture — and the same history until 1950.At that time, living standards were similar, probably a little higher in theNorth. Today, best estimates indicate that GDP per capita in the South ismore than 15 times that of the North. The huge difference in performancesurely reflects the huge difference in institutions between the countries: theform of government and the nature of economic activity.

In other cases, policies may play an important role. We think of policiesas less fundamental aspects of the economic environment than institutions.An honest judicial system is an institution, but tax rates and governmentspending are policies. There’s a fuzzy line between the two, but the idea isthat policies are more easily changed than institutions.

Peter Henry (our dean) and Conrad Miller illustrate the role of policies in acomparison of Barbados and Jamaica. We’ll draw liberally from their paper.They note that the two countries have similar backgrounds and institutions:

Both [are] former British colonies, small island economies, andpredominantly inhabited by the descendants of Africans.... Asformer British colonies, Barbados and Jamaica inherited almostidentical political, economic, and legal institutions: WestminsterParliamentary democracy, constitutional protection of propertyrights, and legal systems rooted in English common law.

Nevertheless, Barbados grew 1.3 percent a year faster between 1960 and2002, giving it a substantially higher standard of living. (This difference islarger than it looks — the power of compound interest and all that.)

http://www.aeaweb.org/articles.php?doi=10.1257/aer.99.2.261


One clear difference between the two countries was their macroeconomicpolicies. In the 1970s, Jamaica increased government spending on job cre-ation programs, housing, food subsidies, and many other things. When taxrevenue failed to keep up, the government found itself with large, persistentbudget deficits, which they financed by borrowing from the central bank.This, in turn, led to inflation rates of 20 percent and higher. A fixed ex-change rate raised the price of Jamaican goods relative to imports, whichled to restrictions on imports and wage and price controls.

Barbados also had a fixed exchange rate, but combined it with fiscal dis-cipline, monetary restraint, and openness to trade. The result was a verydifferent macroeconomic outcome. It’s possible other factors played a role,too, but in this case policies were arguably as important as institutions.

Executive summary

1. Good institutions are the primary source of good economic performance.

2. A short list would include: governance, rule of law, property rights, andopen competitive markets.

3. Stable and predictable macroeconomic policies matter, too.

Review questions

1. Foxconn’s next frontier. Hon Hai Precision Industry Co. Ltd. (“Fox-conn”) is a Taiwan-based manufacturer that makes products for Apple,Intel, Sony, and others. Known for its plants in China, including one inShenzhen that makes iPads, it also has operations in Brazil, Malaysia,Mexico, and other locations.

With wages rising rapidly in China, Foxconn is exploring other locations.As a private consultant, you have been asked to write a short reportoutlining the advantages and disadvantages of locating in Thailand andVietnam and to compare both to China. You collect the information inTable 6.1 and begin your report.

(a) Which of these indicators are most important to your venture? Howdo the two countries compare on them?

(b) Which country or countries would you recommend to your clients?What are the primary challenges they would face?

Answer. This is a qualitative question, but here’s an outline of what ananswer might look like. A good answer should put some structure on theanalysis, not simply list what’s in the table.


Indicator China Thailand Vietnam

GeneralGDP per capita (2005 USD) 8400 9200 3500Doing Business overall (percentile) 50.8 90.3 46.5World Economic Forum overall (percentile) 80.0 73.6 47.9

GovernancePolitical stability (percentile) 25.0 16.5 52.8Govt effectiveness (percentile) 60.7 59.7 45.0Regulatory quality 45.5 56.4 29.4Rule of law 41.8 48.8 39.9Control of corruption (percentile) 30.3 43.6 33.6

LaborMinimum wage (USD per month) 204 118 65Severance after 10 years (weeks of pay) 43 50 43Labor market efficiency (percentile) 71.5 47.2 64.6Literacy (percent of adults) 94 94 93Years of school (adults) 8.2 7.5 6.4

Infrastructure and tradeInfrastructure quality (percentile) 66.7 68.1 34.0Export documents required (number) 8 5 6Export delay (days) 21 14 21Export cost (USD per container) 580 585 610

Table 6.1: Institutional indicators for China, Thailand, and Vietnam. Per-centiles range from 0 (worst) to 100 (best). Sources: Penn World Table,World Economic Forum, World Bank, Governance Indicators, Doing Busi-ness.

(a) If you build a plant in another country, you’ll be concerned withoverall institutional quality, property rights (whether the govern-ment might steal the plant), labor cost and quality, labor marketinstitutions, and the challenges of exporting your product. There’sno clean link to the indicators, but you might guess that propertyrights would be related to the governance indicators, esp politicalstability and the rule of law. The labor indicators obviously addressconcerns with labor. Infrastructure and trade address the challengesof exporting.

As a rough guide:

• Overall: It’s interesting that Doing Business rates Thailand high-est, but the World Economic Forum rates China highest. And thedifferences are large. In the real world, this would call for a closer


look. Ditto the source of political instability in Thailand.

• Property rights and overall: Thailand looks a bit better than theothers on Control of Corruption and Rule of Law, Vietnam looksbetter on Political Stability.

• Labor cost and quality: Vietnam is considerably cheaper than theother two, if we use GDP per capita or the minimum wage asrough guides to wages. Literacy is similar in the three countries,China is highest, and Vietnam lowest, on education.

• Labor institutions: The World Economic Forum ranks China high-est, and Thailand lowest, on overall labor market efficiency. An-other thing that’s worth a closer look. Severance looks similar.

• Exporting: cost and delay look similar, but Vietnam has the worstinfrastructure. You’ll want to look into this, see what aspects ofthe infrastructure are likely to affect you.

(b) They both look like reasonable candidates. For Thailand, we wouldlook closer at political stability, see what that represents and thinkabout how it would affect us. (And that’s an understatement!) ForVietnam, we would look closer at infrastructure.

2. Business analytics in the EU. As a graduating MBA at the prestigiousecole des Hautes Etudes Commerciales (HEC) de Paris, you face a daunt-ing job market. Together with two classmates, you start developing plansfor a business analytics startup. The idea is to provide data insights to abroad range of businesses located throughout the European Union. Thebeauty of the plan, you think, is that you can do it anywhere. The threeof you have begun to compare the pros and cons of Paris, Barcelona, andStockholm, your respective home bases. You collect the data in Table 6.2and begin to sketch out a plan.

(a) What features do you need in a city to make it attractive to you andyour business?

(b) What are the pros and cons of each city along these dimensions?

(c) Which city do you think best fits your plans?

Answer. This question is less than black and white, here is one possibleanswer.

(a) You need, among other things: an environment friendly to startups,access to the internet and related infrastructure, and possibly a poolof well-educated talent. There are other things, but these seem likethe important ones.

(b) How do they stack up?

• Paris: looks good on ease of starting a business, as well as easeof doing business in general; ditto education; questions/concerns


Country Indicators France Spain Sweden

Ease of doing business (rank) 38 52 14Ease of starting a business (rank) 41 142 61Protecting investors (rank) 80 98 34Getting electricity (rank) 42 62 9Resolving insolvency (rank) 46 22 20Minimum wage (USD/month) 778 1009 noneMandatory severance (weeks of pay) 4 14 noneUnemployment rate 10.5 24.4 7.4Employment rate 64.3 55.8 74.7Difficulty of dismissals (index, 1-6) 2.6 2.0 2.5Education of workers (years) 12.6 11.5 12.5Internet quality (Ookla, index) 81.3 84.0 86.9

City Indicators Paris Barcelona Stockholm

Quality of life (rank, Mercer) 34 44 20Cost of living (index) 226 223 157

Table 6.2: Business indicators for three cities and countries.

about getting electricity and internet quality; the same for cost ofliving.

• Barcelona: huge red flag over ease of starting a business; concernswith getting electricity.

• Stockholm: looks good on overall ease of doing business, gettingelectricity; solid on ease of starting a business; highest internetquality of the three; and lowest cost of living.

(c) Stockholm looks like the clear choice. It would take a good argumentto suggest otherwise. Also highly rated for quality of life, which issomething you definitely want to consider.

The World Economic Forum has a similar take: “Sweden has man-aged to create the right conditions for innovation and the knowledge-based economy. The education system is of high quality and seemsto deliver the right skills. But it should address its labor marketregulations and high tax rate, which are considered the two mostproblematic factors for doing business.”

Update. Since using this as an exam question, we’re learned two things.One is that rent control in Stockholm makes it virtually impossible tofind a place to live — unless you have enough money to buy. The otheris that Berlin might be better than all of these places. A friend in thebusiness tells us that rents are low and there’s a huge amount of technicaltalent available from central Europe at modest cost.



The comparison of Barbados and Jamaica comes from Peter Henry andConrad Miller, “A tale of two islands.”

Here are some other good reads, in order of increasing length:

• Ben Bernanke, “Lessons from emerging markets.” Nice short summary ofwhat good institutions and policies look like.

• Nicholas Bloom and John Van Reenan, “Management practices acrossfirms and countries.” They connect productivity to management prac-tices, including monitoring, targets, and incentives. Some find this obvi-ous, but we find it reassuring that good management has a measurabledifference on performance.

• Bill Easterly, The Elusive Quest for Growth. Essentially a collection ofessays on topics related to helping poor countries, unusually witty for aneconomist.

• David Landes, The Wealth and Poverty of Nations. Less witty than East-erly, but he gives us an interesting historical perspective on the majorcountries of the world: Europe, India, China, etc.

The idea of good institutions has been around forever, or close to it, but wenow have better measures of institutional quality than we used to. One ofthe leading sources is the World Bank’s Doing Business, available at

http://www.doingbusiness.org/.

The reports of the Economist Intelligence Unit are thoughtful aggregatorsof this kind of information.

http://www.aeaweb.org/articles.php?doi=10.1257/aer.99.2.261

http://www.federalreserve.gov/newsevents/speech/Bernanke20110928a.htm

http://www.aeaweb.org/articles.php?doi=10.1257/jep.24.1.203

http://www.aeaweb.org/articles.php?doi=10.1257/jep.24.1.203

http://www.amazon.com/Elusive-Quest-Growth-Economists-Misadventures/dp/0262550423

http://www.amazon.com/Wealth-Poverty-Nations-Some-Rich/dp/0393318885

http://www.doingbusiness.org/

7Labor Markets

Tools: Labor supply and labor demand diagrams; simple model of unem-ployment dynamics.

Key Words: Labor force; employment; unemployment; vacancies; acces-sions and separations.

Big Ideas:

• Employment and unemployment rates summarize the labor market statusof the adult population.

• Labor market institutions and policies affect employment, unemployment,and job creation.

• Unemployment and vacancy rates tell us about excess supply and demandin labor markets. Unemployment arises from the time it takes to matcha worker and with an appropriate job and firm.

Some of the most important markets for aggregate economic performanceare those for labor and (financial) capital, which affect every industry andproduct. Countries differ markedly in their treatment of both markets, with(evidently) different outcomes as a result.

Our focus here is on labor markets. We describe in broad terms what well-functioning markets might look like and compare them to the kinds of in-stitutions and regulations we see around the world.

87


7.1 Indicators of labor-market “status”

Most countries collect extensive labor-market data. This includes measuresof employment, unemployment, and, sometimes, detailed information aboutflows of workers in and out of jobs.

We’ll start with what are called indicators of labor-market status: whetheran individual is working, unemployed, or something else. The first suchindicator is the population, a count of the total number of people in a givengeographic area. Strangely enough, numbers like this are estimates: Wedon’t know exactly how many people there are in the US, Canada, or China,but statistical agencies come up with estimates by a number of methods,typically based on surveys. For most labor-market statistics, the startingpoint is the adult population. Countries differ in their definitions of an adult.The US counts anyone 16 or over, the OECD counts people between the agesof 16 and 64 (“working age”).

The next step is to identify the labor-market status of everyone in the adultpopulation: (i) employed (has a job), (ii) unemployed (not working butwould like to), and (iii) inactive or not in the labor force (everyone else).Category (ii) is a little fuzzy: How do we know whether or not someonewants to work? In some countries, the answer comes from a survey in whichthe person is asked whether he or she is actively looking for a job. In others,only people claiming unemployment benefits are classified as such.

Information on the labor-market status of individuals leads to statistics onthe labor force, the employment rate, the participation rate , and the un-employment rate. The employment rate is the ratio of employment to theadult population. The labor force is the number of people in categories (i)and (ii): either working or unemployed. The participation rate is the ratioof the labor force to the adult population. The unemployment rate is theratio of the number of people who are unemployed to the labor force.

The details here are important. We see large differences, for example, inemployment rates across countries. In Germany and Japan, for example,the employment rate has averaged about 71 percent over the last decade,and in Italy about 57 percent, according to the OECD. The source of thisdifference lies primarily in the number of inactive people, not the number ofunemployed. For that reason, and because it’s easier to measure, many ofthe experts focus on employment rather than unemployment. Newspapers,of course, tend to do the opposite.

In the US, employment data are collected and reported monthly by theBureau of Labor Statistics. The BLS releases its closely-watched monthly

7. Labor Markets 89

report, “The Employment Situation,” at 8:30 am on the first Friday of themonth. It includes such indicators as employment (“nonfarm payroll”), theunemployment rate, and the size of the labor force. This release is basedon two surveys, the Current Employment Statistics (CES) survey of firms’payroll records and the Current Population Survey (CPS) of households.The CES covers 300,000+ businesses and provides detailed industry dataon employment, hours, and earnings of workers on nonfarm payrolls. Themost closely watched number in the US is probably the monthly estimateof the change in nonfarm employment, which comes from this survey. TheCPS covers 60,000+ households and is conducted for the BLS by the Bu-reau of the Census. It provides a comprehensive body of data on labor-forcestatus: employment, unemployment, and so on. Both sets of data are up-dated periodically as more information comes in. Since the two sources areradically different, they occasionally result in conflicting information aboutsuch basic indicators as the number of people employed.

Other countries collect similar data, but the sources and definitions vary.

7.2 Supply and demand for labor

Differences in the abilities and skills of individuals make labor markets in-credibly complex, but we can get a sense of the impact of government reg-ulation in a model in which there is a single market for a single kind oflabor.

Demand for labor. The demand for labor comes from (typically) firms.The short version: The higher the wage, the fewer employees firms will hire.

A more complex version follows from thinking through a hypothetical firm’sdecision-making process. Let us say our firm produces output using theproduction function Y = AF (K,L) = AKαL1−α (“Cobb-Douglas ”). Letus say, for the sake of simplicity, that the capital stock is some fixed numberK. How does the firm’s profit depend on the choice of labor input L? If pis the price of one unit of output and w is the price (wage) of one unit oflabor, the firm’s profit is

Profit = pY − wL− Fixed Costs

= pAF (K,L)− wL− Fixed Costs.

How does profit vary with L? The fixed costs might be attributed to capitalor other factors, but they do not vary with L. For this reason, they won’taffect the demand for labor. What is affected by L is output (which, in turn,affects sales revenue) and cost (the wage bill).


If the firm maximizes its profit, it will add labor as long as the marginalbenefit is greater than the marginal cost. We learned earlier that we cancharacterize the solution to the firm’s maximization problem by computingthe derivative of the profit function and setting it equal to zero. Afterarranging terms, we see that maximum profit occurs when the marginalbenefit of an additional unit of labor (more revenue) equals its marginalcost (the wage):

pA∂F (K,L)

∂L= w.

This is an equation we can solve for L and represents the amount of laborthe firm will hire (demand) for any given values of p, w, and K. In theCobb-Douglas case, Y = AKαL1−α, the demand function follows from

p(1− α)AKαL−α = w,

which implies (solve for L)

L = K

[p(1− α)A

w

]1/α. (7.1)

The aggregate (total) demand for labor is the sum of demands across allfirms. Its important feature, for our purposes, is that it falls when the wagerises, just as we assume most demand functions do. (This property followsfrom the diminishing marginal product of labor, one of the conditions weimposed on the production function.)

Supply of labor. Now let’s turn to the supply of labor. The short version:Supply increases with the wage.

A more complete version goes like this. When selling their labor services,individuals make two decisions: whether to work at all and, if so, how much.Obviously, many jobs offer limited flexibility on the second dimension. Forthis reason, and also because it simplifies the analysis, we will ignore thesecond choice and consider the decision of an individual deciding whetheror not to work a given number of hours h. What is the gain from working?The monetary gain is wh. However, what matters for the individual is theincrease in happiness, or satisfaction, that such pay induces. This may varyacross individuals. For example, the same pay may be more valuable to apoor individual than to a rich one. What is the loss from working? Simple!He has less time to dedicate to other activities, including playing bridge orfootball, cooking, reading economics books, or spending time with family.The value of these activities is what economists call the reservation wage.For any wage less than this, the benefits of not working are greater than thebenefits of working. For the economy as a whole, the higher the wage, the

7. Labor Markets 91

greater the number of people who decide to work. Thus, aggregate laborsupply Ls increases with the wage rate w.

Labor-market equilibrium. We represent labor demand and supplywith straight lines in Figure 7.1. The equilibrium wage rate w∗ is the valueat which demand and supply are equal. The number of workers employed atthis wage defines the level of employment L∗. This kind of analysis shouldbe familiar to anyone who has taken an economics course.

Figure 7.1: Equilibrium in the labor market.

-L

6w Z

ZZZZZZZZZZZZZZ Ld

""""""""""""""" Ls

L∗

w∗

Where is unemployment in Figure 7.1? We might think of L∗ as representingboth employment (the number of people hired by firms, since the point ison their demand curve) and the labor force (the number of people whowant to work at the going wage). Unemployment is the difference betweenthese two numbers, so evidently there is none. There is an almost perfectanalogy between this market and a dealer-type securities market such as theNasdaq. At the Nasdaq, dealers post bid and ask prices and are committedto executing transactions at those prices. If you want to sell a given security,you just contact one of the dealers (or ask your broker to do this for you).If you’d like to sell at less than the bid, you have a deal. There are no“unemployed” securities.

7.3 Supply and demand with a minimum wage

There are many reasons that labor markets don’t work quite like our fric-tionless market. Let’s look at one: government policies and institutions.Examples include minimum wages, restrictions on wage adjustments, laborunions, limits on hiring and firing, and so on. We don’t argue that these


Figure 7.2: The labor market with a minimum wage.

-L

6w Z

ZZZZZZZZZZZZZZ Ld

""""""""""""""" Ls

A B

C

D

E

F

L∗

w∗wm

things are bad — they may very well have benefits — but they do have animpact on how the labor market works.

We’ll look at the minimum wage since it’s the simplest example. (Remem-ber: Simple is a good thing.) If we prohibit purchases of labor servicesbelow a given wage, how does the market work? Figure 7.2 shows how thesupply-and-demand analysis might be applied in this case. In the figure,the minimum wage (wm) is higher than the equilibrium wage (w∗). At theminimum wage, the supply of labor (the line segment EB) is greater thanthe demand for labor (the line segment EA). Minimum wage laws don’tforce firms to hire, so employment is given by their demand function. Thedifference between supply and demand is unemployment (the line segmentAB). In the figure, unemployment is represented by the line segment AB.The unemployment rate is the ratio of unemployment (AB) to the supply oflabor (EB). As a practical matter, it’s an open question whether the impactof the minimum wage on unemployment is large or small, but few economistsdoubt that it’s there.

Who are the winners and losers from the minimum wage? The winnersare the employed, who get a higher wage than they would otherwise. Thelosers are the unemployed (who would prefer to work) and firms (who mustpay more for labor). Taken as a whole, the policy reduces welfare by anamount represented by the triangle ACD. This will seem clear if you recallhow welfare triangles work, mysterious otherwise, but it’s true in this settingthat a minimum wage reduces overall welfare.

7. Labor Markets 93

7.4 Labor-market institutions

The minimum wage is a useful illustration, but labor-market institutionsand regulations differ dramatically across countries along many dimensions.Some of them have been collected and reported by the World Bank’s DoingBusiness. They report, for most countries in the world, the flexibility anemployer has over the terms of employment, including the employer’s abilityto vary hours, the cost and difficulty of dismissal, and whether workerscan be hired under fixed-term (as opposed to permanent) contracts. Somecountries also limit hours (no more than 25 hours a week!) or give unionsmore power over the terms of employment contracts.

The evidence suggests that many kinds of labor-market regulation have theultimate effect of reducing employment. There is, of course, a useful rolefor laws that enforce fair dealing. Paying workers for fewer hours than theyworked, for example, is impossible to justify. But many labor-market regu-lations seem to discourage firms from hiring, although their stated purposeis to “protect jobs.” Restrictions on layoffs and mandatory severance pay-ments seem to do this since they raise the long-term cost of hiring workers.In many countries, we’ve seen growth in the number of part-time and unof-ficial workers, precisely to get around this kind of regulation.

7.5 Labor-market flow indicators

The supply and demand diagram is indicative, but it can’t address one of themost striking features of modern economies: the huge amount of turnoverwe see in labor markets. Economies create and destroy jobs at truly amazingrates. Even MBA graduates often find themselves changing jobs frequently,either by choice (they find jobs they like better) or by misfortune (economicdownturns, mergers, and so on).

In the aggregate, we see this in data from both firms and households. Atfirms, new positions are created either because existing firms expand theiroperations or because new firms hire workers. We refer to this phenomenonas job creation. At the same time, existing firms sometimes eliminate po-sitions. We refer to this process as job destruction. An establishment (aproduction unit, such as a factory or store) is said to create jobs if it in-creases the number of positions between one period and the next. Theeconomy’s overall job creation is the sum of the increases in positions acrossall the establishments that created jobs. Similarly, an establishment is saidto destroy jobs if it decreases its number of positions from one period to thenext. The economy’s overall job destruction is the sum of the decreases injobs across all establishments that destroyed jobs. The sum of job creation


and job destruction is referred to as job reallocation or job turnover. Jobcreation, destruction, and reallocation rates are ratios of job creation, de-struction, and reallocation, respectively, to the total number of jobs in theeconomy. These rates vary greatly across countries, but their magnitudesare impressive everywhere.

We see similar turnover in household data, with individuals reporting fre-quent changes in jobs or employment status. An employed individual canstay in her job, move to another job, become unemployed (leave one jobbut look for another), or leave the labor force (leave one job without seek-ing another). Similarly, an unemployed person can become employed (get ajob), stay unemployed (look for a job without taking one), or leave the laborforce (stop looking for a job). Someone out of the labor force can becomeemployed (take a job), become unemployed (look for a job without takingone), or remain out of the labor force. We have information from surveyson each of these possible changes.

Some summary measures will give you a sense of how this looks for a typi-cal individual. Accessions occur when individuals take new jobs, regardlessof their current status. Separations occur when individuals leave jobs, re-gardless of their reason. The accession and separation rates are ratios ofaccessions and separations, respectively, to total jobs. The sum of the tworates is referred to as the worker reallocation rate. In the late 1980s, theannual accession rate in the US was 45.2 percent and the annual separationrate was 46.0 percent. The worker reallocation rate was a staggering 91.2percent! These numbers do not say why workers change jobs, merely thatthey do. Worker reallocation rates are generally lower in other countries,including France (59.6 percent) and Italy (68.1%). Apparently, it is morecommon in the US both to leave a job and to take a new job. You might askyourself whether the factors that make the separation rate high also makethe accession rate high, or whether they are influenced by different factors.

7.6 Virtues of flexible input markets

There’s a big-picture point hidden here somewhere. In a modern economy,the mix of products is changing constantly. Many of the products andservices we use today simply weren’t available twenty years ago: high-speedinternet access, iPods, databases, and so on. A successful economy needsa mechanism to shift capital and labor to these new uses and away fromothers. The evidence suggests that countries with labor and capital marketsthat do this well tend to perform well in the aggregate. The ability of aneconomy to reallocate jobs across firms, industries, and geographical areasis, perhaps, even more important than capital. Sometimes, labor-market

7. Labor Markets 95

institutions are an obstacle to this reallocation process, reducing aggregateproductivity and output.

Most developed economies have gone through at least one major reallocationin their history, as most people shifted from agriculture to industry. In theUS, there’s been a further shift from manufacturing to services. Servicesseem less vivid than physical goods to most of us, but the fact is that goodsrepresent a smaller part of modern developed economies than services do.You might ask yourself what sector you’re likely to go into. Past experiencesuggests that few of our students are targeting jobs in manufacturing, muchless agriculture.

If reallocation is important, then labor-market institutions are central to ag-gregate performance. If people cannot be shifted quickly to more-productivesectors and firms, aggregate productivity will be lower. Consider the impactof an increase in productivity in a single industry. What is the impact onemployment? The immediate effect is probably to throw some people out ofwork, since a smaller number of people can produce the same output. Theemployment impact depends on the elasticity of demand: If the elasticityis low, the increase in productivity reduces employment. The long-term ef-fect is to reallocate these workers to other sectors. We would argue thatthis is good for the economy as a whole, even if it’s painful for the peoplewho had reallocation forced on them. Nevertheless, there’s a long historyof concern about reallocation, dating back at least to the machine-smashing“Luddites.”

Deregulation is similar, in the sense that it often leads to reallocation ofcapital and labor. Consider an example from Europe. In recent years, theEuropean airline market has gone through a deregulation process resemblingthat of the US in the 1980s. Before deregulation, every European countryhad its own national airline. The airline was typically a monopolist oninternal routes and a (collusive) duopolist (with the other country’s airline)on international routes. Like many monopolists, these airlines charged highprices and operated inefficiently. Now, any company can fly any route in theEuropean Union. The entry of new carriers has meant big trouble for manyof the incumbents. Sabena and Swissair went bust. Others (Alitalia?) mayfollow suit. It is clear that at the end of the reorganization of the industry,fares will be much lower (they are already, as a matter of fact). As a result,people will fly more often, and there may even be more jobs in the industry.Along the way, job destruction by the incumbents will be accompanied byjob creation by the new entrants.

Who gains? Consumers and workers in new firms. Who loses? The workersand shareholders of incumbent firms. Traditional welfare analysis tells us


that the gains are greater than the losses, but the political process does notnecessarily weight them equally. In fact, the costs are often concentrated,while the benefits are thinly spread over many individual consumers andfirms, so the political process will tend to give greater weight to the former.Nevertheless, it’s likely that such a reallocation is a net benefit to the societyas a whole.

7.7 A model of unemployment dynamics

These flows suggest a more dynamic labor market than our supply-and-demand analysis. Where do they come from? You might consider your owncase: What factors might cause you to leave a job? take a new one? A simplemodel can help us understand the overall impact of individual decisions likethis on economy-wide employment and unemployment rates. To keep thingssimple, we will ignore transitions in and out of the labor force and focus onemployment and unemployment.

To start, individuals may be either unemployed, U , or employed, E, withU + E = L and L a fixed number. The unemployment and employmentrates are then u = U/L and e = E/L. Since the only states are U and E,the employment and unemployment rates sum to one: u+ e = 1.

The unemployment rate can change over time if individuals change theirlabor-market status. Let us say that a constant fraction 0 < s < 1 (sfor separation) of employed people lose their jobs and become unemployed.Why might this be? Perhaps because their firms are doing poorly, and eithershrink or go out of business altogether. Let us also say that a constantfraction 0 < a < 1 (a for accession) of unemployed people find new jobs,as they find employers who need their skills. We’ve seen that this kind ofreallocation is the norm for modern economies. With these two ingredients,the unemployment rate changes like this from one period to the next:

ut+1 = ut + set − aut

or∆ut+1 = set − aut.

Unemployment rises over time if more employed people lose their jobs thanunemployed people find new jobs, and it falls over time if the reverse is true.(Formally, this should remind you of the dynamics of capital accumulationin the Solow model). Since ut + et = 1, we can write this as

∆ut+1 = s(1− ut)− aut. (7.2)

This is useful because we have summarized the dynamics of unemploymentin a single equation. If you were told that the unemployment rate was now

7. Labor Markets 97

(say) u0, then repeated application of (7.2) would enable you to calculatethe unemployment rate in future periods. It would be a very simple matterto do these calculations in Excel.

Using equation (7.2), we can compute both the period-by-period dynamicsand the steady-state unemployment rate. We find steady-state unemploy-ment (u, say) by setting ∆ut+1 = 0 so that

0 = s(1− u)− au.

Solving for u gives

u =s

s+ a,

a number between zero and one. Over time, the unemployment rate “gravi-tates” to this value, so we might also refer to it as the “long run” or “natural”unemployment rate. The idea is that we want a measure of the underlyingunemployment rate that would prevail if it were not for temporary shocksthat make u0 6= u. Clearly, steady-state unemployment is higher when s, theseparation rate, is higher and is lower when a, the accession rate, is higher.That is, if people lose jobs easily and have difficulty finding them, then theunemployment rate will be higher.

You should think of the parameters of this model, a and s, as standingin for various country-specific labor-market policies and institutional ar-rangements that affect the willingness of firms to hire and fire workers, thewillingness of workers to take and quit jobs, and so on. Examples of suchpolicies include: minimum wages; taxes on labor income; regulations thatcontrol the length of the working week (such as the 35-hour week in France);the size of severance payments for layoffs; the size of unemployment bene-fits; and so on. Which of these policies decrease a? Which of these policiesdecrease s?

Here is a different way to look at the steady-state calculation. With alittle bit of statistics, one can show that an individual’s average duration ofunemployment in this model is 1/a, and an individual’s average duration ofemployment is 1/s. Steady-state unemployment is given by

u =s

s+ a=

1a

1a + 1

s

=duration of U

duration of U + duration of E.

So, to think about why European unemployment is relatively high comparedto that of the US, we might begin with factors that either increase theduration of unemployment or reduce the duration of employment. Which ofthese factors do you think is more important for European unemployment?


7.8 Institutions and labor-market dynamics

We can get a sense of the dynamics of labor-market reallocation by puttingour earlier labor-market analysis to work. In our model, the accession andseparation rates also govern the response of the unemployment rate to ashock that pushes unemployment above (or below) its steady-state value.In particular, these rates govern the speed of adjustment back to the steadystate. To see this, write the equation governing the dynamics of the unem-ployment rate as

ut+1 = s+ [1− (s+ a)]ut.

In order for the model to be empirically realistic, we need a worker reallo-cation rate, s+ a, that satisfies

0 < s+ a < 1.

With a little bit of algebra, the unemployment rate can be written in termsof deviations from its steady-state value

ut+1 − u = λ(ut − u),

where λ = 1− (s+ a) is the speed of adjustment of the unemployment rateto its steady-state value. The reason for this is that with a little bit morealgebra one can show that if the unemployment rate is hit by a temporaryshock (that does not affect a or s) that takes on the value u0, the adjustmentback to steady state is given by the formula

ut − u = λt(u0 − u)

orut = (1− λt)u+ λtu0.

What’s important is not the algebra but the idea: In economies with lowvalues of s and a, worker reallocation is slow. Here, we see that this resultsin slow adjustment of the unemployment rate. But you can imagine, aswell, slow reaction of producers to consumer preferences. The churning ofthe labor market implied by high values of s and a, thus, serves a purposeof shifting workers to jobs in which their value is the highest.

Numerical example. Suppose that in both Europe and the US, s = 0.01,and that accession is aUS = 0.19 in the US, but lower in Europe, aEU = 0.09.Then, not only is European unemployment 10 percent as opposed to 5 per-cent in the US, but European unemployment also takes considerably longerto respond to shocks than does US unemployment (λEU = 0.90, λUS = 0.80).Based on this example, can you imagine the economic consequences if, asrecent evidence suggests, the US labor market has become less flexible?

7. Labor Markets 99

Executive summary

1. Labor-market indicators include employment (the number of people work-ing), unemployment (the number not working who would like to), the la-bor force (employment plus unemployment), and the unemployment rate(the ratio of unemployment to the labor force).

2. Measures to protect workers often have the opposite effect; that is, bymaking labor more expensive to firms, they may reduce employment.

3. Many developed economies are characterized by high rates of job andworker reallocation. People change jobs and firms change workers —frequently.

4. The efficiency of work reallocation affects the performance of the economyas a whole. In particular, flexible labor markets help an economy respondto the inevitable changes in products and industries that occur.

Review questions

1. Labor-market indicators. You are the mayor of a small village whoselabor-market data are: adult population (100), employment (55), andunemployment (5).

(a) Draw a circle on a piece of paper corresponding to the population ofyour village. Divide it into sections corresponding to employment,unemployment, labor force, and not in the labor force.

(b) Compute the employment rate, the participation rate, and the un-employment rate.

Answer.

(a) For you to do.

(b) The employment rate is 55 percent [= 55/100]. The participationrate is 60 percent [= (55 + 5)/100]. The unemployment rate is 8.3percent [= 5/60].

2. Supply and demand. Consider an economy with one firm (which is nev-ertheless a price taker). It produces widgets according to the productionfunction Y = AK1/2L1/2 and sells them for two dollars each. [Yes,we know we said α would always be one-third, but apparently we lied.Sorry.] For simplicity, assume that A = K = 1. The supply of labor inthis economy is Ls = w3/2.

(a) What is the demand for labor? How does it depend on the wage?

(b) What are the equilibrium values for the labor force, the wage, andemployment? What is the unemployment rate?


(c) Suppose the government imposes a minimum wage of $1.1. Whatare the equilibrium values for the labor force, the wage, and employ-ment? What is the unemployment rate?

Answer.

(a) The demand for labor is given by Ld(w) = 1[2× (1/2)]/w]2 = w−2.This follows from the labor demand function, equation (7.1).

(b) Equating demand and supply yields L∗ = w∗ = 1. The labor forceis one and the unemployment rate is zero.

(c) With a minimum wage of $1.1, the supply of labor (the labor force)is 1.13/2 = 1.15. The demand for labor is 1.1−2 = 0.826. There-fore, employment is 0.826 and the unemployment rate is (1.15 −0.826)/1.15 = .2817 or 28.17 percent.

3. Minimum wage. Milton Friedman once suggested that the minimumwage discriminated against people with low skills. To see what he hadin mind, consider an environment with two kinds of workers, high-skilledand low-skilled. Suppose each group has its own separate labor market,each subject to the same minimum wage.

(a) Which kind of worker is most likely to be affected by a minimumwage? Why?

(b) Who gains or loses from a minimum wage? Does this explain Fried-man’s comment?

Answer.

(a) You might imagine that high-skilled workers will not be affected bya minimum wage, since their skill demands a wage well above it.But workers with low skill might find that no one is willing to hirethem at the minimum: their skills don’t justify it.

(b) The winners are those with low skill who happen to find jobs. Thelosers are the firms that hire them and, more to the point, the low-skilled who can’t find work. The might get jobs if we allowed thewage to fall. So they bear much of the cost of the system.

4. Taxing labor. Suppose we put a tax on labor, paid by firms. Use a supplyand demand diagram in which the vertical axis is the pretax wage andthe horizontal axis is the quantity of labor.

(a) Draw a supply and demand diagram. What happens to the curveswhen you add the tax?

(b) What is the impact on the pretax wage and quantity of labor?

(a) Draw something like Figure 7.1. When you add the tax, the demandcurve falls by the amount of the tax. The amount of the fall equalsthe tax per unit. [If you put the after-tax wage on the vertical axis,

7. Labor Markets 101

the supply curve would shift, but that’s another story. The point isto be careful about the pre- and post-tax wage.]

(b) Since demand has fallen, so does the pretax wage and the quantityof labor. Put simply: if you tax labor, you would expect firms tobuy less.

5. Layoffs. From the New York Times, March 6, 2009 (rough paraphrase):The WARN Act requires employers to give 60 days’ notice if a plant isclosed or 500 or more people are laid off at one location. Some won-der whether notice should be required for other job losses. A Berkeleyprofessor says it’s a matter of “transparency and decency.” An IBM ex-ecutive disagrees, noting that it’s routine for the company to lay off someemployees while hiring others. “This business is in a constant state oftransformation.” If you were asked to advise the government, how wouldyou describe the costs and benefits of wider application of the WARNAct?

Answer. This is another cost of firing workers, and we know that higherfiring costs tend to discourage firms from hiring workers in the first place.The question is how high the cost is. If we figure workers will keepproducing, it may be small; if not, it’s larger, especially if there’s a chanceof sabotage or other damaging behavior.

We asked two of our favorite management professors the same question.Professor Wiesenfeld said: “I think giving people advanced notice (not60 days, but not escorting them to the door immediately) is generallybeneficial, because it helps to retain the commitment and motivation ofthe person’s former colleagues.” Professor Freedman said: “It dependson the situation. I have encountered situations where people who aregiven notice act in a very destructive manner.”

6. Income support systems. In the US and UK, flexible labor markets areaccompanied by income support systems in which (for example) peoplewith low incomes pay negative income tax; that is, they receive money.In the US, this is referred to as the Earned Income Tax Credit. In whatways is this better than direct intervention in labor markets? Worse?

Answer. Many see this as an effective way to reconcile the benefits of aflexible labor market with a safety net that protects workers from someof the challenges of losing one’s job. Restrictions on firing, for example,help people with jobs keep them, but discourage firms from hiring morepeople. An income support system avoids the latter.

7. Labor-market dynamics. In our model of unemployment dynamics, sup-pose that the accession rate is a = 0.2 and the separation rate is s = 0.01.

(a) Compute the steady-state unemployment rate and the speed of ad-justment parameter.


(b) Suppose that a restriction on firing makes workers less attractive tofirms. What effects might this have on long-run unemployment andthe response of the economy to an increase in the unemploymentrate?

Answer.

(a) The steady-state unemployment rate is u = s/(s+ a) = 0.048 or 4.8percent. The speed of adjustment parameter is λ = 1−(s+a) = 0.79.

(b) This restriction is likely to lower the accession rate a, thereby in-creasing long-run unemployment and making periods of high unem-ployment last longer (i.e., making λ closer to one).


Labor data are less standardized across countries than national income andproduct accounts. The US Bureau of Labor Statistics has a nice collec-tion (unfortunately being phased out) of international data constructed inroughly comparable ways across countries:

http://www.bls.gov/fls/.

Ditto the OECD:

http://www.oecd.org/std/labourstatistics/

http://www.oecd.org/els/emp/keyemploymentstatistics.htm.

Yes, two links! The second includes data on labor market policies and em-ployment protection. The World Bank’s Doing Business also has an exten-sive collection of indicators of labor-market institutions.

Finally, Denmark is a fascinating example when it comes to labor marketssince it combines flexibility (it’s easy to fire people, for example) with gen-erous social support (unemployment insurance and training, for example).A nice overview is Jianping Zhou, IMF working paper, “Danish for All?Balancing Flexibility with Security.”

http://www.bls.gov/fls/

http://www.oecd.org/std/labourstatistics/

http://www.oecd.org/els/emp/keyemploymentstatistics.htm

http://www.imf.org/external/pubs/ft/wp/2007/wp0736.pdf

7. Labor Markets 103

Symbols and data and used in this chapter


Symbol Definition

p Price of outputw Wage of one unit of labor (say, one hour)Y OutputK Stock of physical capitalL Quantity of laborA Total factor productivity (TFP)α Exponent of K in Cobb-Douglas production function

(= capital share of income)F (K,L) Production function of K and LL∗ Equilibrium level of employmentw∗ Equilibrium wagewm Minimum wageLs Labor supplyLd Labor demandU Unemployed personsE Employed personsu Unemployment rate (= U/L)e Employment rate (= E/L)s Separation rate (share of people who lose a job)a accession rate (share of people who find a job)∆xt+1 Change of xt+1 (= xt+1 − xt)u Steady-state unemployment rateu0 Unemployment rate in start-period zeroλ speed of adjustment of unemployment rate to steady state



Variable Source

Nonfarm employment PAYEMSUnemployment rate UNRATEEmployment ratio EMRATIONonfarm openings rate JTSJORDuration of unemployment UEMPMEANU6 unemployment rate U6RATECivilian labor force CLF16OVCivilian participation rate CIVPART

To retrieve the data online, add the identifier from the source columnto http://research.stlouisfed.org/fred2/series/. For example, toretrieve nonfarm employment, point your browser to http://research.

stlouisfed.org/fred2/series/PAYEMS


http://research.stlouisfed.org/fred2/series/PAYEMS


8Financial Markets

Key Words: Time consistency; information asymmetry.

Big Ideas:

• Effective financial markets require strong institutional support.

• Good institutions deal with information asymmetries and time consistencyissues.

Some of the most important markets for aggregate economic performanceare those for labor and (financial) capital, which affect every industry andproduct. Countries differ markedly in their treatment of both markets, with(evidently) different outcomes as a result.

Our focus here is on financial markets, which are, perhaps, the most difficultmarkets to manage effectively.

8.1 Features of effective financial markets

Financial markets are central to economic performance, because they facil-itate (if they work well) the allocation of resources to the most-productivefirms. In the US today, some firms borrow from banks, others issue bondsand equity in capital markets, and still others raise money through venturecapitalists. Countries differ widely in how they do this, but they all haveways of channeling funds from households (savers) to firms (borrowers).

The primary issue with financial markets is information, and we know thatmarkets sometimes handle information poorly. Here, investors need to un-derstand the risks faced by borrowers, but borrowers typically know more

105


about themselves than others do. A bank, for example, needs to knowenough about its borrowers to assess the risk of default, and its depositorsneed to know enough about the bank’s ability to do this well to assess therisk to their deposits. A bank (or other financial institution) is, therefore,in the information business: Its goal is to process information efficiently sothat it can assess and manage risk.

None of this is easy to do. All of these financial arrangements require insti-tutional support. An effective financial system requires some version of:

• Creditor protection. If A lends money to B, it’s essential that A’sclaim be honored. That requires a legal system that makes the credi-tor’s rights clear and enforces them if necessary. (You might think about“property rights” and the “rule of law” about now.) Without this, peoplewill either not make loans or will make loans only to friends and relatives.Weak, ineffective financial systems follow naturally when creditors are notprotected, and economic performance suffers as a result.

• Corporate governance. The laws of most countries give creditorssome say over the management of firms. Equity investors, for example, arerepresented (in principle) by boards of directors. There’s endless debateabout how best to do this, but there’s no question that doing it well isimportant.

• Disclosure. When people invest in securities, they need to understandwhat they’re buying. In most countries with active securities markets,the law dictates disclosure of relevant financial information. Again, somecountries do this better than others.

• Central banks. Most countries have central banks. If run well, theyplay an important role in the economy, particularly as lenders of last resortduring financial crises.

Measures of these things are available from a number of sources, includ-ing the World Bank’s Doing Business website, particularly the categoriesGetting Credit and Protecting Investors.

8.2 Financial regulation and crises

From the perspective of a country, one of the challenges of managing financialmarkets is that they can cause enormous collateral damage if something goeswrong. If a farmer goes bankrupt, you buy milk from someone else. But if alarge financial institution goes under, it can slow down the whole economy.The question is how to manage financial markets to get the benefits of athriving financial system with the least risk.

http://www.doingbusiness.org/

8. Financial Markets 107

No one yet has come up with a perfect answer. An unregulated financialsystem may work well most of the time, but will experience occasional crises.A more tightly regulated system may (it’s not a sure thing) have lowercrisis risk, but the regulation may distort the allocation of capital. Mostapproaches to financial regulation face a tradeoff of this sort.

Consider deposit insurance. In the US, bank panics were a common occur-rence up through the 1930s. During the Depression, thousands of bankswent under. Some of them were insolvent. Others closed because depositorsdemanded their money back for fear that the bank would go under: whatwe call bank runs. It’s a consequence, in part, of people having imperfectinformation about the bank’s soundness.

The solution — or, rather, one solution — was to provide deposit insurance.Milton Friedman and Anna Schwartz called federal deposit insurance “themost important structural change” made in the 1930s to deal with bankruns. And it worked — bank runs pretty much ended.

But like many solutions, it raised new problems. The problem with depositinsurance is what economists call “moral hazard” and others might call the“other people’s money” problem. Since depositors don’t face the risk oflosing their money, banks don’t face the risk of withdrawal, and they haveless reason to control the risk of their investments. Or to put it differently,their borrowing costs don’t reflect the risk of their loan portfolios. So theytake excessive risk, which is hardly what we’re looking for. Therefore, weadd to deposit insurance some regulatory oversight intended to limit banks’ability to take risks. We know from bitter experience that it’s hard to getthis right, and we’re still trying.

A related challenge is the “too big to fail” dilemma, a classic version of thetime-consistency problem discussed in Chapter 6. Policymakers insist thatthey will never bail out failing banks, but everyone knows in advance thata failed behemoth can topple the financial system (think Lehman or AIG).So the promise lacks credibility: a future policymaker is likely to bail themout anyway. Investors know this, and reward the largest intermediaries withlow funding costs, thereby subsidizing excessive risk taking.

Executive summary

1. Financial markets work best when based on effective institutions.

2. It’s hard to get that exactly right.



The logic and operation of financial institutions is a huge subject in its ownright. Among the courses we have on the topic are Professor Schoenholtz’s“Money and Banking,” course ECON-GB.2333, and “Financial Crisis andPolicy,” course ECON-GB.2343. Or see his book: Stephen Cecchetti andKermit Schoenholtz, Money, Banking and Financial Markets; or visit theirblog at http://www.moneyandbanking.com. Ben Bernanke’s testimony toCongress (search “Bernanke testimony”) is a wonderful overview of financialregulation and the 2008 crisis. He also did a series of lectures that are postedon the Fed’s website.

Beyond that, financial crises make good reading, and there’s no shortage ofgood books on the subject. One of the best reads is Edward Chancellor’sDevil Take the Hindmost , a history of financial speculation. On the mostrecent crisis, we enjoyed David Wessel’s In Fed We Trust and Andrew RossSorkin’s Too Big to Fail .

http://www.amazon.com/dp/007802174X/

http://www.moneyandbanking.com

http://www.amazon.com/FED-We-Trust-Bernankes-Great/dp/0307459691/

http://www.amazon.com/Too-Big-Fail-Washington-FinancialSystem/dp/0143120271/

9International Trade

Tools: Ricardo’s model of trade; consumption and production possibilityfrontiers.

Key Words: Absolute advantage; comparative advantage; autarky.

Big Ideas:

• Trade is a positive-sum game: both countries benefit.

• Gains from trade are similar to increases in TFP: trade increases aggregateconsumption opportunities.

• Trade creates winners and losers, but the winners win more than the loserslose. Trade affects the kind of jobs that are available, not the number ofjobs.

Virtually all economists, liberal or conservative, believe that free (or “free-er”) trade is a good thing: good for consumers, good for workers, good for allcountries involved. Why? Because consumers are able to buy products fromthe cheapest vendor, which forces production to the highest productivityfirms, which, in turn, supports the highest wages for workers.

No one else seems to believe that. Most are convinced that one side of tradeis unfair, that one country is gaining at the other’s expense. The purposeof this chapter is to outline the logic for trade. The logic is mathematical,by which we mean it’s clear and precise, if a little abstract. You can decidefor yourself whether you find it persuasive.

109


9.1 Ricardo’s theory of trade

David Ricardo was one of the most influential economists of the early nine-teenth century, but he came to economics by accident. Born to a Jewishfamily in Amsterdam, he left the Netherlands and broke off relations withhis family (and they with him) to avoid an arranged marriage, and marrieda Quaker instead. He set himself up in London as a government securitiesdealer and became, in his words, “sufficiently rich to satisfy all my desiresand the reasonable desires of all those about me.” Looking for something tooccupy his time, he developed the modern theory of international trade.

Many people in Ricardo’s day (and ours) regarded trade as a zero-sum ac-tivity: If you gain from trade, then I must lose. His insight was that bothsides typically benefit, even if it appears that one has an absolute productiv-ity advantage over the other. In his words, each country has a comparativeadvantage.

We develop Ricardo’s theory in a particularly simple setting: Two coun-tries produce and consume two products, and both products are producedwith labor alone. In many respects, this version of the theory is unrealis-tic, but the lack of realism is exactly what makes the analysis simple andunderstandable. None of the simplifications are essential to the argument.

To be specific, let us call the countries the US (country 1) and Mexico(country 2) and the products apples and bananas. (Yes, we know neitherthe US nor Mexico produces many bananas, but we like the letters a andb.) We start by specifying the productivity levels: the quantities of product(either a or b) in country i (either 1 or 2) produced with one unit of labor.We’ll use specific numbers, which we report in Table 9.1. Let us say, alsoin the interest of simplicity, that the labor force is the same in the twocountries: L1 = L2 = 100.

Table 9.1: Productivities for trade example.

Apples Bananas

US (country 1) α1 = 20 β1 = 10Mexico (country 2) α2 = 5 β2 = 5

The productivities mirror the discussion you hear about trade between arich country (the US here) and a poor one (Mexico). For example, oneunit of labor produces more in the US whether it’s used to produce applesor bananas. We would say the US has an absolute advantage in producingboth goods. A number of factors might play a role here. Perhaps the weather

9. International Trade 111

is better, labor is better educated, the distribution system is more efficient,or the institutions are better.

The question is: Would Mexico and the US both benefit from completelyfree trade, relative to a position of autarky (no trade at all)? The an-swer is yes, but let’s run through the argument. Suppose Mexico had highenough tariffs or other barriers to kill off trade altogether. Then Mexicowould likely produce both products. How much of each? It could pro-duce apples in quantity a = L2α2 = 100 × 5 = 500 or bananas in quantityb = L2β2 = 100 × 5 = 500. It could also produce any combination in be-tween, as shown in Figure 9.1 (the solid line). We call the solid line theproduction possibility frontier for Mexico, since every point on the line rep-resents a possible production/consumption combination. In this example,the line has a one-for-one tradeoff between apples and bananas, implying arelative price of q = pb/pa = α2/β2 = 1.

What happens if Mexico and the US allow trade? It depends on the relativeprice q. Suppose that Mexico can export bananas at a relative price of q > 1apples for each banana. Then Mexico will produce only bananas. Why?Because it can produce each at the same cost (1/5 = 0.2 units of labor), butbananas sell for more on the world market. As a country, it faces strictlybetter possibilities if it trades rather than producing both goods itself. If itproduces only bananas (b = 500) and then trades some for apples at a rateof q apples for every banana, it does better than the one-for-one tradeoff itgot from producing apples itself. (See the dashed line in Figure 9.1, whichis above the solid line.) [As a check on your understanding: How would thiswork if q < 1? What would Mexico produce? What would its possibilityfrontier look like? Would Mexico still benefit from trade?]

In short, trade benefits Mexico, even though it is less productive than theUS for both products. Similar reasoning shows that the US would benefitfrom trade, too. [Another check: What is the possibility frontier for the USif there’s no trade? Trade with q > 1? Trade with q < 1?]

Ricardo had a rationale for these gains from trade: Even though Mexicois less productive absolutely (α1 > α2 and β1 > β2), it is comparativelymore productive in bananas than the US (β2/α2 > β1/α1). Conversely, theUS is comparatively more productive in apples (α1/β1 > α2/β2). If eachcountry produces the good for which it is comparatively more productive,then world productivity rises and both countries benefit. For this reason,Ricardo referred to this as the theory of comparative advantage.


Figure 9.1: Gains from trade in Mexico.

-

6

a

b

Possibilities with trade

Possibilities without trade

@@@@@@@@@@@@@@@

500

500

9.2 Digging a little deeper

Moving to free trade is similar to an increase in productivity because whenyou shift production to high productivity products, aggregate productivityrises. The impact is similar to our discussion of labor and financial mar-kets. Countries with good labor and financial markets allocate inputs moreeffectively and increase aggregate productivity as a result. This is a naturalfeature of trade models, but it takes some effort to work out the details,even in a setting as simple as our example. If you’re averse to math, youmight skip to the next section the first time through.

Our goal is to compare production and consumption in two cases: one withno trade, and one with completely free trade (no tariffs or transportationcosts). The comparison is somewhat extreme, but the hope is that it will giveus the flavor of less-extreme moves toward freer trade. In each case, we needto find the competitive equilibrium. Competitive means that consumers andproducers take prices as given. (No monopolies allowed here!) Formally, acompetitive equilibrium is a set of prices and quantities that satisfies threeconditions:

1. Consumers are on their demand curves; they buy what they want at thegiven prices.

2. Producers make zero profits (the effect of competition).

3. Total production equals total consumption for each product.


Finding an equilibrium can be difficult, particularly if you have a low thresh-old for algebra, but we can readily verify a proposed equilibrium by checkingthe three conditions.

Consumers. The citizens of each country consume apples and bananas.They also work for the firms, getting a wage w for each unit of labor. Eachconsumer (we can index them by i) earns an income yi = wli (for simplicity,we assume that li is given). Obviously, L =

∑i li. How do consumers

spend their income? Like any of us, they receive satisfaction (or utility)from consuming both apples and bananas. Let us say that their utility fromconsumption is given by the following function:

U(a, b) = asb1−s.

Given her income and prices for apples and bananas, each consumer willmake spending decisions that maximize her utility. Simple calculations showthat a consumer will spend a fraction s of her income on apples and thecomplementary fraction 1 − s on bananas. Summing across all consumers,we find that a fraction s of national income Y (Y =

∑i yi = w

∑i li = wL)

is spent on apples, and the remainder is spent on bananas:

paa = sY

pbb = (1− s)Y.

These are (effectively) the demand functions for the two products. We’llassume below that s = 0.75 in both countries.

Producers. Consider producers in a specific country. Let’s say that laborsells for w per unit, with w potentially differing across countries. A producerof apples (say) will hire labor at cost w per unit and sell apples, getting aprofit of

Profit = a(pa − w/α),

where α is apple productivity in the country we’re examining. If pa < w/α,the price is too low and no apples will be produced. If pa > w/α, competitionamong apple producers will drive the price down until pa = w/α. In short,if apples are produced, their price will be pa = w/α. Similarly, if bananasare produced, their price will be pb = w/β. If both apples and bananas areproduced (and they need not be), their relative price will be q = pb/pa =α/β.

Equilibrium without trade. If there’s no trade, then each country willproduce both products. Let us say that the wage rate is w = 1 in bothcountries (but not comparable, because they may be measured in differentunits). Since the total labor input is 100 in either country, national income


is Y = wL = 1 × 100 = 100 in both Mexico and the US (again, the unitsare not comparable). In the US, prices will be

pa = w/α = 1/20 = 0.05

pb = w/β = 1/10 = 0.10

q = pb/pa = 2.

At these prices, the demands for apples and bananas are, respectively,

a = sY /pa = 0.75× 100/0.05 = 1500

b = (1− s)Y /pb = 0.25× 100/0.1 = 250.

Total utility is, therefore, U = a0.75b0.25 = 958.

What about Mexico? Using similar methods, we find that prices are

pa = w/α = 1/5 = 0.20

pb = w/β = 1/5 = 0.20

q = pb/pa = 1.

Demands are a = 375, b = 125. Utility is U = 285. The numbers aresummarized in Table 9.2 for future reference.

Equilibrium with trade.

The complete solution is reported in Table 9.2, but let’s see where it comesfrom. It’s moderately complicated, so skip directly to the next section unlessyou’re incredibly curious. The objective is to find prices and wages thatequate supply and demand for apples, bananas, and labor in both countries.We’ll focus on bananas; if the banana market clears, so do the others.

Let’s guess (we made up the example, so our guesses are pretty good) thatthe US produces only apples and Mexico produces only bananas. In this way,the two countries specialize in the production of the good in which they havea comparative advantage. We’ll verify this guess later. Let’s think abouthow the banana market works. Supply is whatever Mexico produces givenits available labor L2 and productivity β2:

Supply of Bananas = L2β2.

What about demand? This is more complicated. Since each country spendsa fraction 1− s on bananas, total demand is

Demand for Bananas = (1− s)Y1/pb + (1− s)Y2/pb,


Table 9.2: Prices and quantities with and without trade.

Free Trade No Trade

US

Price of apples pa 0.05 0.05Price of bananas pb 0.0667 0.10Wage w 1 1 (dollar)Consumption of apples a 1,500 1,500Consumption of bananas b 375 250Utility 1,061 958

Mexico

Price of apples pa 0.05 0.2Price of bananas pb 0.0667 0.2Wage w 0.3333 1 (peso)Consumption of apples a 500 375Consumption of bananas b 125 125Utility 354 285

In the no-trade case, the wages are normalizations; they’re in differentunits and are not comparable across countries.

where Y1 and Y2 are incomes in the US and Mexico, respectively. Competi-tion in labor and output markets will equate income paid to workers to thevalue of output they produce:

Y1 = L1α1pa

Y2 = L2β2pb.

Why? Because competition drives profits to zero. That gives us

Demand for Bananas = (1− s)L1α1pa/pb + (1− s)L2β2.

Equating supply and demand and doing some algebra gives us

pb/pa =(1− s)L1α1

sL2β2. (9.1)

Plugging in numbers, we find pb/pa = 4/3. If you’re unusually curious, youcan show (using the same approach) that supply and demand are equal forapples at the same price.

We can now get a sense where the relative price of bananas comes from:supply and demand! On the supply side, higher productivity for bananas(higher β2) drives the price down. This is the usual shift out of the supply


curve. Similarly, higher apple productivity (higher α1) makes apples rela-tively less expensive. On the demand side, lower s indicates a lower desirefor apples and a higher desire for bananas and, thus, drives the price ofbananas up. This is essentially a rightward shift of the demand curve.

Finally, we verify that the US produces only apples, Mexico only bananas.How do we show this? At these prices and wages, US banana producers losemoney — so they don’t produce any. Ditto Mexican apple producers — thewage rate supported by banana production is too high for apple producersto break even, so they won’t produce either. This is really a good thingfor Mexican workers, as producing bananas supports a higher standard ofliving.

9.3 Wages and productivity

In the US you sometimes hear: “US workers can’t compete with Mexicanworkers, because their wages are so low.” In Mexico, you sometimes hear:“Mexican workers can’t compete with US workers, because their productiv-ity is so much higher.” Who is right? The answer, of course, is neither.In our model, wages reflect productivity. Mexican wages are lower becauseMexican workers are less productive. Their wage is low enough to (just)make up for their lower productivity. Ditto American workers: Firms hirethem despite their higher wage because their productivity is higher. Thevalue of labor to a firm is a balance between the two forces: price andproductivity.

We can be more specific about the connection between productivity andwages. As a rule, the wage ratio will be somewhere between the productivityratios for the two products. In this case, the ratio of the US to the Mexicanwage will be between 2 (= 10/5, the ratio of banana productivities) and 4(= 20/5, the ratio of apple productivities):

2 = β1/β2 < w1/w2 < α1/α2 = 4.

If we were to (somehow) force up the Mexican wage above the upper bound,we would simply make Mexican bananas more expensive to Americans thanproducing them locally would. Demand for Mexican labor would dry up.Similarly, if we were to force down the Mexican wage below the lower bound,Mexico would find it profitable to produce both goods. However, demandfor Mexican labor would exceed supply, which you’d expect to increase itsprice.

Overall, wages are connected to productivities. Between the two bounds,demand plays a role, as we’ve seen. If people have a stronger desire forbananas, that tends to benefit the Mexican workers who produce them byincreasing the price of bananas, as we see in equation (9.1).


9.4 Bottom line

Let’s think about the calculations summarized in Table 9.2 from a non-technical perspective. The numbers make several points that extend tomore-general settings:

• Trade makes consumers (=workers) better off. In the US, con-sumption of apples stays the same and consumption of bananas increases.As a result, utility rises from 958 to 1061. In Mexico, consumption ofbananas does not change, but consumption of apples is larger. There-fore, utility rises from 285 to 354. In more-realistic models, the impactof trade is typically small, but both countries gain, as they do here. It’sa byproduct of Adam Smith’s invisible hand (aka the first theorem ofwelfare economics), which you might recall from microeconomics.

• Trade changes production. In this case, Mexico shifted out of applesinto bananas, and the US did the reverse. In other models, the changein production may not be so extreme, but it’s generally true that theypredict that every country will stop producing some products and importthem instead. The result is a more efficient system of production, as eachcountry produces those goods for which its relative productivity is thehighest.

• Trade raises productivity. Both effects show up in macroeconomicdata as increases in productivity. If we were NIPA people, we mightcompute GDP this way: sum production of apples and bananas, valued ata consistent set of prices. In this case, we’ll use the free-trade prices, whichis similar to PPP adjustment (apply the same prices in every country).GDP at world prices is

Free Trade No Trade

US 100.0 91.7Mexico 33.3 27.1

Once trade shows up in GDP, it shows up in aggregate productivity, too.We don’t have capital in this model, so the production function is Y = AL.Since L is unchanged across trade regimes, the change in Y reflects anincrease in TFP.

• No jobs are lost — or found. In our example, every unit of labor isused whether trade was possible or not. This is only a little extreme: Notrade models suggest that trade will have much impact on employment.Any effect there might be comes from the impact on labor supply of anincrease in the wage. So when you read the newspaper, especially in an


election year, remember that trade has an impact on what the jobs are,not on how many there are.

9.5 Winners and losers

From what we’ve seen, trade is a wonderful thing. Who could be againstit? In fact, lots of people seem to have a passionately held view that tradeand globalization are a plague on the world. What could they be thinking?What follows is a short list of their arguments. In practice, our experienceis that most arguments against trade are simply self-interest in disguise.

Externalities. This is a classic “failure” of markets, the (unpriced) im-pact of one person’s decision on another’s utility. For example, a pollutingproducer may inflict bad air on you and reduce your welfare. When talkingabout trade, people often refer to positive external effects on productivity.Are there advantages to having a local industry beyond the profit and loss?Could it help others to increase their efficiency? This is a legitimate argu-ment, but probably not a good one in most cases. Moreover, it’s typicallyused by firms and industries looking for special deals from their governments.For example, European car makers used this argument when seeking govern-ment protection from Japanese and Korean imports. Their argument wasthat the domestic producers generated technology spillovers that benefitedrelated industries.

Differences among residents of a country. We rushed over it, but builtinto our example was that all citizens of a country have the same tastesand the same productivity in the workplace. In practice, this is not true,and trade will affect each person differently. In the example summarized inFigure 9.1, all Mexican consumers are better off. Now suppose that Mexicansdiffer in how much they like apples and bananas (i.e., the parameter s is notthe same across individuals). In this case, the ones who like apples less andbananas more may be worse off since the relative price of bananas has goneup with free trade. In short, there can be losers. What the theory says,however, is that the winners win a lot more than the losers lose — Mexicansgain, on average. In principle, you might want to take some of the winners’gains and give them to the losers, but in practice this isn’t that easy to do.

Another example shows up regularly in the press: people who lose their jobswhen production adjusts to trade. In this case, suppose that you workedfor an apple producer and lost your job. The long-term answer is: Get ajob working for a banana producer, since their productivity is higher. Butin the short run, there’s no question that you suffer a loss from losing yourjob. Also, if working for a banana producer requires skills that you do not


have, you might have to retrain yourself. Again, the winners should be ableto compensate the losers and still be better off, but in practice it rarelyhappens. More importantly, people lose jobs all the time for lots of reasons,and trade is unlikely to be a major factor in most cases.

Concentrated and dispersed interests. One of the political challengesis that the gains from trade are often concentrated in a small group of firmsor people. That makes them a natural political force. Suppose, for example,that five people lose $1 million each from unrestricted trade by one millionpeople gain $10 each. The gains ($10m) outweigh the losses ($5m), butthe one million people who benefits are less likely to change their votes orotherwise express an opinion on the issue than the five people who lose amillion each.

Executive summary

1. International trade allows consumers to buy products more cheaply andworkers to take jobs where their productivity is highest.

2. There can be both winners and losers from trade, but, in theory at least,the winners gain more than the losers lose.

Review questions

1. Gains from trade. In Mexico, how does consumption of apples and ba-nanas change when we move from No Trade to Free Trade? Are Mexicanworker better off? Who in Mexico loses?

Answer. We read from Table 9.2. Consumption of apples rises from 375to 500, and consumption of bananas stays the same at 125. So Mexicans(who are both workers and consumers) are better off. No Mexicans losehere, but you might imagine in a different world that the former Mexicanproducers of apples suffer. What we know in general is that the gainsoutweigh any such losses.

2. Trade politics. Although the logic for trade is clear, politicians all overthe world complain about “unfair” competition from abroad. Why?

Answer. It’s hard to see this as anything but protection of their sup-porters. In addition, people don’t vote in other countries’ elections. Inour example, you can imagine Mexican apple producers asking their gov-ernment to protect them from US competition. What they should dohere is switch to bananas, but the the political process often favors thewell-connected over the average worker or consumer.


3. Changing demand. In the example, show that an increase in s to 0.78 isgood for US workers and bad for Mexican workers. Why might that be?

Answer. This increases the price of the product produced by US workers,which improves their situation. The opposite is true for Mexican workers.We say that the “terms of trade” (relative price of their export good) havemoved against them. Think of an oil-exporting country: An increase inthe price of oil is good for them, bad for importers. [Duh!]

4. Could there be losers? If trade eliminates apple-producing jobs in Mexico,could apple producers and workers be worse off?

Answer. Yes! But the gains for others are typically larger than theselosses, so we should be able to compensate the losers and leave everyonebetter off. This is trickier than it sounds, though.

5. Food prices and trade. When food prices rose sharply in 2008, Indiarestricted food exports to keep prices down. Who would you expect tobenefit from this policy? Lose? Is the overall impact on the Indianeconomy likely to be positive or negative?

Answer. You might expect this to keep prices down in the short runbecause we’ve reduced the demand for locally produced food. (You couldalso express this as an increase in supply to the domestic market, butit’s cleaner this way.) Who gains? Domestic food buyers and foreignproducers. Who loses? Domestic sellers/producers and foreign buyers.Generally, any market intervention like this is a net loss. You could showthis formally using a supply and demand diagram.


Doug Irwin’s “History of trade policy” is a nice overview of two centuries ofthought on trade issues.

http://www.econlib.org/library/Columns/Irwintrade.html

Part IIIShort-Term Economic Performance

121

Short-Term Overview

This outline covers key concepts from the second part of the course: short-term economic performance. It is not exhaustive, but is meant to help you(i) anticipate what is coming and (ii) organize your thoughts later on.

Business Cycle Properties

Tools: Basic statistics: standard deviation, correlation.

Key Words: Volatility; procyclical and countercyclical.

Big Ideas:

• Economies do not grow smoothly or regularly. We refer to the fluctuationsin economic activity as business cycles.

• Growth rates of expenditure components move up and down with GDPover the business cycle, but they move by different amounts. Spending oninvestment and consumer durables moves more than output; we say it ismore volatile. Spending on services and nondurable goods is less volatilethan output. Labor and capital markets move with the cycle as well.

Business-Cycle Indicators

Tools: Basic statistics (standard deviation, correlation); cross-correlationfunction.

Key Words: Volatility; procyclical and countercyclical; leading, lagging,and coincident.

123


• Business cycle indicators are characterized by several properties: procycli-cal and countercyclical, leading and lagging.

• Cross-correlation functions identify these properties.

Money and Inflation

Tools: The quantity theory; central bank balance sheet; open market op-erations.

Key Words: Price level; inflation; hyperinflation; quantity theory; velocity;fiscal dominance.

Big Ideas:

• Inflation is the growth rate of the price level, which is typically measuredby a price index.

• The quantity theory links the money supply with the price level and out-put. In the long run, an increase in the money supply results in an increasein the price level (inflation).

• Hyperinflation refers to an inflation rate of 100% per year or more. Hy-perinflations follow a standard pattern: government deficits are financedwith money, which produces inflation. We call this fiscal dominance overmonetary policy.

Aggregate supply and Demand

Tools: Aggregate supply and demand (AS/AD) graph.

Key Words: Short- and long-run aggregate supply; sticky wages; aggregatedemand; supply and demand shocks; Keynesian.

Big Ideas:

• The AS/AD model relates output and prices in the short and long runs.The model is composed of (i) an upward-sloping short-run aggregate sup-ply curve, which inherits its shape from sticky wages; (ii) a vertical long-run aggregate supply curve; and (iii) a downward-sloping aggregate de-mand curve.

• Shocks to the aggregate supply and demand curves have different effectson inflation and output.

125

Policy in the AS/AD model


Key Words: Policy objectives; potential output; output gap.

Big Ideas:

• The objectives of monetary policy are generally thought to be (i) stableprices and (ii) output near its long-run equilibrium level.

• A direct consequence is that monetary policy should respond differentlyto demand and supply shocks. As a general rule, policy should resist/offsetchanges in output triggered by shifts in demand and accommodate/reinforcechanges triggered by shifts in supply.

• We can identify supply or demand shocks from whether output and pricesmove together or in opposite directions.

Money and Interest Rates

Tools: Open market operations; central bank balance sheet; Taylor rule.

Key Words: Real interest rate; nominal interest rate; expected inflation;real money balances; inflation targeting; interest-rate rules; rules vs. discre-tion; zero lower bound; quantitative easing; credit easing; policy durationcommitment.

Big Ideas:

• In conventional practice, central banks use open market operations tomanage interest rates. These policy actions are equivalent to managingthe money supply directly.

• The Taylor rule provides a guide to how central banks manage their targetinterest rates in response to data on inflation and (real) GDP growth.

• When interest rates are at or near zero, a central bank can resort to un-conventional monetary policy, including quantitative easing, credit easing,and policy-duration commitments. These policies have been in widespreaduse since 2008.


10Business-Cycle Properties

Tools: Basic statistics: standard deviation, correlation.

Key Words: Volatility; procyclical and countercyclical.

Big Ideas:

• Economies do not grow smoothly or regularly. We refer to the fluctuationsin economic activity as business cycles.

• Growth rates of expenditure components move up and down with GDPover the business cycle, but they move by different amounts. Spending oninvestment and consumer durables moves more than output; we say it ismore volatile. Spending on services and nondurable goods is less volatilethan output. Labor and capital markets move with the cycle as well.

Over the last two centuries, US real GDP has grown at an average ratebetween 3 and 3.5 percent a year, but this growth has been anything butsmooth. Annual growth rates over the last fifty years have ranged from−2 percent or less (in 1975, 1982, and 2008) to 8 percent (in 1966 and1984). These short-term “fluctuations” or “business cycles” (we’ll use theterms interchangeably) are the subject of intense interest by businesses andplay an important role in their decisions to hire, produce, and invest. Andit’s not just the US; although we will use US data, other countries exhibitsimilar volatility. Emerging markets, including the US in the 19th century,differ primarily in having greater volatility. The bottom line: Fluctuationsin economic growth are a fact of life.

Our mission is to outline some of the basic features of these fluctuations,which point to ways of dealing with the inevitable risk and uncertainty theybring to our lives.

127



10.1 Cycles and volatility

Arthur Burns and Wesley Mitchell, two of the pioneers of business-cycleresearch, noted:

business cycles are a type of fluctuation found in the aggregateeconomic activity of nations. ... A cycle consists of expansionsoccurring at about the same time in many economic activities,followed by similarly general recessions, contractions and revivalswhich merge into the expansion phases of the next cycle; thissequence of changes is recurrent but not periodic; in durationbusiness cycles vary from more than one year to ten or twelveyears.

(From: Measuring business cycles, NBER, 1946.)

You can get a sense of these economy-wide fluctuations from Figure 10.1,where we plot real GDP and its year-on-year growth rate — the rate ofgrowth of quarterly GDP over the same quarter a year earlier. As some-one once said: The variance is so large that you hardly notice the mean.The figure also suggests that volatility was lower between 1985 and 2007.People used to refer to this as the “great moderation,” but that seems lessappropriate now.

Figure 10.1: Level and fluctuations of US real GDP.

050

0010

000

1500

0

U.S

. dol

lars

(bi

llion

s)

1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 2020q1

-50

510

Yea

r-on

-yea

r gr

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1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 2020q1


10. Business-Cycle Properties 129

The National Bureau of Economic Research, which dates business cyclesin the US, defines a recession as “a significant decline in economic activityspread across the economy, lasting more than a few months, normally visiblein real GDP, real income, employment, industrial production, and wholesale-retail sales.” Using subjective methods, they identify dates of peaks andtroughs. Less formally, many people use the rule of thumb that a recessionconsists of two consecutive quarters in which GDP has fallen. The year-on-year growth rates in the figure don’t coincide exactly with this definition, butyou can see the eight official NBER recessions since 1960 as sharp downwardspikes in GDP growth.

10.2 Expenditure components

Burns and Mitchell refer to fluctuations in “many economic activities.”Among these activities are the expenditure components of GDP. Are theirfluctuations similar to those of GDP? On the whole, the components, par-ticularly consumption and investment, move up and down together, but themagnitudes differ enormously. Consumption currently accounts for nearly70 percent of US GDP; as you might expect, its fluctuations are similar (seeFigure 10.2). The correlation of year-on-year growth rates in consumption(total) and GDP is 0.84.

Table 10.1 shows us that consumption’s components — services, nondurablegoods, and durable goods — also vary with GDP, but their correlations and(especially) volatilities differ somewhat. Consumption of nondurables andservices is less volatile than GDP, in the sense that the standard deviationof its growth rate is smaller. Consumption of durables is far more volatilethan consumption of nondurables and services. You might think of specificproducts and industries that reflect the same phenomenon. Why do youthink cars and refrigerators are more volatile than haircuts and medicalcare?

Investment also moves up and down with output and is substantially morevolatile (see Figure 10.2). As a rule of thumb, a one-percent increase in GDPis associated with about a three-percent increase in total investment. (We’relooking at the ratio of standard deviations here, and the high correlation ofthe two series.) Table 10.1 shows that the major components of investment— structures, equipment, and residential housing — are highly correlatedwith, and more volatile than, GDP.

When we turn to business-cycle indicators, we’ll see that many of them aremore detailed measures of some aspect of consumption or investment. Con-sumption is important because it accounts for most of GDP. Investment isimportant because it is highly responsive to changes in economic conditions.

http://www.nber.org/cycles/main.html

http://research.stlouisfed.org/fred2/series/PCECC96?cid=110

http://research.stlouisfed.org/fred2/series/GPDIC96?cid=112


Table 10.1: Properties of business cycles.

Std Dev (%) Corr w/ GDP

GDP 2.19 1.00Consumption: total 1.75 0.84Consumption: services 1.22 0.63Consumption: nondurable 1.65 0.75Consumption: durables 6.29 0.76Investment: total 6.64 0.86Investment: structures 7.85 0.46Investment: equipment 7.35 0.81Investment: housing 13.05 0.60Employment 1.77 0.76S&P 500 Index 14.98 0.36

Numbers refer to year-on-year growth rates computed from quarterlyUS data.

Figure 10.2: Fluctuations in consumption, investment, and GDP.

GDP

Consumption

Investment

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Yea

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1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 2020q1

10.3 Labor and capital markets move with the cycle

Labor markets also move with the business cycle; indeed, it’s the way inwhich business cycles make themselves known to us most directly. Fig-ure 10.3 shows us how fluctuations in employment covary with GDP. Notethat employment growth is generally less than GDP growth; the differencereflects an increase in output per worker — a good thing, to be sure! You



can see in the figure that the ups and downs in employment typically lagthose in GDP by a little — a quarter or two. The current expansion isan extreme case, with GDP rebounding well before employment, but thegeneral pattern is not unusual.

Figure 10.3: Fluctuations in employment and GDP.

GDP

Employment

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1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 2020q1

Figure 10.4: Fluctuations in asset prices and GDP.

GDP

S&P 500

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1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 2020q1

Financial (capital) markets move with the business cycle, as well. Figure10.4 plots the growth rate of real GDP against versus the yearly growth


rate of the S&P 500 index. Notice that aggregate stock prices are extremelyvolatile, with a standard deviation about eight times larger than GDP. More-over, aggregate stock prices and GDP are positively correlated (0.36). Thissuggests that good news about the economy is good news for stock prices.It’s hard to see in Figure 10.4, but we’ll see later that stock prices leadGDP; the correlation of stock prices with GDP two quarters later is above0.5. Financial measures often lead economic activity. Another example isthe yield curve (the difference between long-term and short-term interestrates), which tends to flatten or invert ahead of business downturns. We’lllook at this more closely when we turn to indicators.

Labor markets and asset prices are both sources of useful indicators of eco-nomic activity. We’ll see more of each shortly.

Executive summary

1. Economies do not grow smoothly; they exhibit lots of short-term volatil-ity.

2. Spending on investment goods (by firms) and consumer durables (byhouseholds) are more volatile than output as a whole. Household spend-ing on nondurable goods and services is less volatile than output.

3. Most variables are procyclical; that is, they move up and down with GDP.Examples include consumption, investment, employment, and the stockmarket.

Review questions

1. Statistics. What statistic would you use to show that two economic seriesmove up and down together?

Answer. The correlation between them. Table 10.1, for example, in-cludes the correlations of year-on-year growth rates of GDP and severalexpenditure components. The correlations in most cases are above 0.8,indicating they do indeed mostly move up and down together.

2. More statistics. What statistic would you use to show that one series ismore “volatile” than another.

Answer. The standard deviation. In the same table, we saw that invest-ment is more volatile than consumption in the sense that its standarddeviation is about three times higher.

3. Do it yourself. Reproduce Figure 10.3 in FRED. The variables are realGDP (FRED code GDPC1) and nonfarm employment (PAYEMS).

http://research.stlouisfed.org/fred2/series/SP500



These basic features of business cycles are covered in most macroeconomicstextbooks. A reasonably good overview is Finn Kydland and Edward Prescott,“Real facts and a monetary myth.”

Data used in this chapter


Variable Source

GDP GDPC1Consumption PCECC96

Services PCESVC96Durables PCDGCC96Nondurables PCNDGC96

Investment GPDIC96Nonresidential PNFIC96

Equipment NRIPDC96Housing PRFIC96

Employment PAYEMSS&P500 SP50010yr Treasury yield GS102yr Treasury yield GS2Federal funds rate FEDFUNDS

To retrieve the data online, add the identifier from the source columnto http://research.stlouisfed.org/fred2/series/. For example, toretrieve nonfarm employment, point your browser to http://research.

stlouisfed.org/fred2/series/PAYEMS

http://www.minneapolisfed.org/publications_papers/pub_display.cfm?id=225





11Business-Cycle Indicators

Tools: Basic statistics (standard deviation, correlation); cross-correlationfunction.

Key Words: Volatility; procyclical and countercyclical; leading, lagging,and coincident.

• Business cycle indicators are characterized by several properties: procycli-cal and countercyclical, leading and lagging.

• Cross-correlation functions identify these properties.

Probably the leading use of macroeconomic data (and macroeconomists)is forecasting: predicting future movements in economic variables so thatbusinesses can decide how much to produce, investors can decide how toallocate their assets, and households can decide how much to spend. Thegood news is that forecasting is possible; we’re not simply throwing darts ata board. The bad news is that it’s not easy; even the best forecasters arefar from perfect.

This chapter is devoted to short-term business-cycle indicators — variablesthat indicate changes in near-term economic conditions — and how to usethem. In principle, we could be interested in many features of the economy:output, inflation, interest rates, exchange rates, and so on. We’ll focus onoutput, but the methods can easily be applied to other variables. We lookat the US, but similar ideas and methods apply to any country with reliabledata.

135


11.1 Terminology

We refer to the properties of economic indicators with two related sets ofterms. One set of terms describes whether an indicator’s movements tend tocome before or after movements in output. We say an indicator leads outputif its ups and downs typically precede those of output, and lags output if theycome after. An indicator whose movements are contemporaneous with thoseof output is referred to as coincident . Thus, the adjectives leading, lagging,and coincident describe the timing of an indicator’s movements relative tothose of output. Looking ahead, you might guess that leading indicatorsare most useful in forecasting. The stock market, for example, is a commonleading indicator; it leads output by six to eight months, as we’ll see shortly.

A second set of terms refers to whether an indicator’s movements are posi-tively or negatively correlated with output. If the correlation is positive, wesay it is procyclical ; if the correlation is negative, we say it is countercycli-cal . Most indicators are procyclical: employment, stock prices, housingstarts, and so on. The most common countercyclical indicators have todo with unemployment: Both the unemployment rate and new claims forunemployment insurance rise during recessions.

11.2 Forecasting

The classic forecasting problem goes something like this: What do we expectthe value of [some economic variable] to be k periods in the future? Here, kis any period of time you like, but we’re usually interested in anything fromnext week to a few years in the future.

If we’re forecasting GDP, there’s an extra difficulty because we don’t knowthe present or the recent past, much less the future. We’ve seen, for example,that fourth-quarter GDP is first reported near the end of the following Jan-uary, and even that number is a preliminary estimate. From the perspectiveof mid-January, then, we need to “forecast” the previous quarter.

We’re going to shortcut this difficulty (somewhat) by using the monthlyIndustrial Production (IP) index as a substitute for real GDP, but the issueis a general one, in that the time lag in getting data is both an issue in itsown right and a constraint on forecasting the future. IP measures outputin manufacturing, mining, and utilities. More important, its fluctuationsare strongly correlated with those in GDP. You can see that in Figure 11.1,which compares year-on-year growth rates in GDP and IP (aggregated toa quarterly frequency). You will notice that IP is more volatile than GDPbut otherwise follows its ups and downs reasonably well. You may also

http://research.stlouisfed.org/fred2/series/INDPRO?cid=3

11. Business-Cycle Indicators 137

Figure 11.1: US GDP and industrial production.

GDP

Industrial production

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e (a

nnua

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1960q1 1970q1 1980q1 1990q1 2000q1 2010q1 2020q1

notice some differences between them in the recent past, which have beentraced to the rising importance of services in the US economy. In the US,IP is reported by the Federal Reserve in the middle of the following month.Data for December, for example, are available in mid-January. Using IP,therefore, gives us a shorter information lag than GDP. In addition, themonthly frequency gives us a finer time interval for near-term forecasting.For both reasons, we will focus our discussion of forecasting on IP ratherthan, GDP, although the same principles apply to both, as well as to othermacroeconomic and financial variables.

11.3 Good indicators

Good forecasts require good inputs. One way to forecast a variable is withits own past. Future growth rates of IP, for example, might be related tocurrent and past growth rates. We can usually do better than that by addingother indicators to our analysis. Speaking generally, a good indicator shouldhave one or more of these properties:

• Correlation. A good indicator is correlated with the variable we areforecasting.

• Lead. A good indicator leads the variable we are forecasting.

• Timeliness. A good indicator is available quickly.


• Stability. A good indicator does not undergo major revisions subsequentto its initial release, and its relationship with the variable we are forecast-ing doesn’t change over time.

On the whole, measures of economic activity (employment, for example)tend to be strong on correlation and weak on timeliness (see the discussionof GDP above) and stability (many economic series are revised frequently).The best ones lead the business cycle. In contrast, financial indicators (eq-uity prices, interest rates) are weaker on correlation but stronger on theother three properties: They’re typically available immediately, often leadthe cycle, and are not revised. Various indexes of leading indicators combinemultiple series with the hope of getting the best from each. The Confer-ence Board’s quasi-official index of leading indicators is the most commonexample.

11.4 Identifying good indicators

How do we identify indicators with high potential? We’ll use another bitof terminology that leads to an extremely useful graphical representation ofthe dynamic relation between two variables: the cross-correlation function(ccf).

You may recall that the correlation between two variables (x and y, say)is a measure of how closely they are related in a statistical sense. If thecorrelation is (say) 0.8, then observations with large values of x tend also tohave large values of y. If the correlation is 0.4, this association is weaker.And if the correlation is –0.8, observations with large values of x tend tohave small values of y — and vice versa.

The cross-correlation function extends the concept of correlation to the tim-ing of two indicators. Specifically, consider the correlation between x atdate t and y at date t − k. If k is negative, then we’re talking about thecorrelation between x now and y k periods in the future. If k is positive, wehave the correlation between x now and y k periods in the past. By lookingat the pattern of correlations, we can identify indicators x that tend to leadthe variable y. We refer to k as the lag of y vs x, but if k is negative it refersto a lead. Mathematically, we write

ccf(k) = corr(xt, yt−k).

Typically, we would graph this against k, with k starting with a negativenumber and moving to positive numbers. The pattern of correlations tellsus whether an indicator x leads or lags (on average) a variable y.


Figure 11.2: Cross-correlations: the S&P 500 and industrial production.

Leads IP Lags IP

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-20 -10 0 10 20Lag in months relative to industrial production

Both series are year-on-year growth rates for the period 1960-present.The large correlations to the left tell us that the S&P 500 index is agood indicator of future industrial production.

Let’s move from the abstract to the concrete to make sure we understandwhat the ccf represents. [You might want to work your way through thisparagraph slowly, it’s important.] We calculate the year-on-year growthrates of the S&P 500 index and industrial production and compute their ccfusing the S&P 500 for x and industrial production for y. Figure 11.2 is aplot of their correlations against the lag k. There’s a lot of information here,so let’s go through it one dot at a time. The dot at k = 0 (on the vertical lineat the center of the figure) shows that the contemporaneous correlation isabout 0.2. Contemporaneous means that we’re looking at the two variablesat the same time: March 2001 industrial production is lined up with March2001 S&P 500, and so on. Next, consider the dot corresponding to k = −10on the left side of the figure. The correlation of (roughly) 0.5 pictured inthe figure shows the growth rate of industrial production with the growthrate of the S&P 500 index dated ten months earlier. Evidently high growthin equity prices now is associated with high growth in IP 10 months later.Finally, consider a dot on the right side of the figure. The dot at k = +10suggests that the correlation of industrial production growth with equityprice growth ten months later is about –0.2.

This pattern of correlations tells us a lot about the timing of movements inthe two variables. In general, negative values of k (the left side of the figure)indicate correlations of the S&P 500 with future industrial production; we

http://research.stlouisfed.org/fred2/series/SP500


would say that they reflect the tendency of stock prices to lead output.Positive values of k (the right side of the figure) indicate correlations ofthe S&P 500 with past industrial production; they reflect the tendency ofstock prices to lag output. What we see in the figure is a strong correlationof the S&P 500 index with industrial production seven to eight monthslater. Evidently, the stock-price index is a leading indicator of industrialproduction.

We’ll use the cross-correlation function to identify whether an indicator isleading or lagging, procyclical or countercyclical.

To do this, we find the largest correlation in absolute value. If it occursto the left of the figure, we say it’s a leading indicator; if on the right,lagging. Similarly, if the (largest) correlation is positive, we say the indicatoris procyclical; if negative, countercyclical. In principle an indicator could beboth leading and lagging, or both pro- and counter-cyclical, but we’ll dealwith that if and when it happens.

Digression. We snuck something in here that we should mention again, although it’s

not particularly important for our purposes. We used year-on-year growth rates instead

of monthly growth rates. We could use either, but the year-on-year pictures are smoother

and, in our view, more attractive. We’d see a similar pattern with monthly growth rates,

but the correlations would be both smaller and choppier.

Let’s look at some other indicators and see which ones lead IP. Some ofthe most common indicators are labor-market variables, constructed by theBureau of Labor Statistics. Cross-correlation functions for four of themare pictured in Figure 11.3. Nonfarm payroll employment (a measure ofemployment constructed from a survey of firm payrolls) is a slightly laggingindicator since the ccf peaks with a lag of one to two months. It is, neverthe-less, useful because the correlation (over 0.8) is unusually strong. And evena two-month lag is more timely than the GDP numbers. The unemploy-ment rate is countercyclical (note the negative correlations) and lags IP inthe sense that the largest correlation comes at a lag of three to four months.It seems that a rise (fall) in output is associated with a fall (rise) in theunemployment rate three to four months later. New applications (“claims”)for unemployment insurance are also countercyclical, but the correlation isstronger than for the overall unemployment rate, and it leads industrial pro-duction by two to three months. Another popular indicator is average hoursworked per week in manufacturing. This indicator is strongly procyclicaland leads industrial production by two to four months. The labor market,in short, provides a good overall picture of the economy and, in some cases,supplies indications of future movements in industrial production. The lead-ing variables (“new claims” and “average weekly hours”) are more highly


http://research.stlouisfed.org/fred2/series/IC4WSA

http://research.stlouisfed.org/fred2/series/IC4WSA

http://research.stlouisfed.org/fred2/series/AWHMAN

http://research.stlouisfed.org/fred2/series/AWHMAN


Figure 11.3: Cross-correlation functions: labor market indicators.

Leads IP Lags IP

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correlated with industrial production than the S&P 500 index, but the leadsare shorter.

Other sources of useful information are various measures and surveys ofeconomic activity conducted by the Bureau of the Census and private or-ganizations. Cross-correlation functions for four common ones are picturedin Figure 11.4. The first two are building permits and housing starts, twoindicators of new home construction reported by the Census. Two ideas liebehind their use: that construction of new capital is more volatile than othersectors of the economy and that decisions to build new homes reflect opti-mism about the future. The cross-correlation functions suggest that theywork; while the correlations are smaller than with (say) employment, theleads are substantial (ten months or so). The next two are popular privatesurveys. Consumer sentiment, based on a survey of consumers collected bythe University of Michigan, reflects consumers’ optimism about current andfuture economic conditions. The purchasing managers index is what we calla “diffusion index.” It’s based on a survey of purchasing managers whoreport whether they see economic activity increasing or decreasing. Each isused as is. We see in the figure that both are procyclical leading indicators.

We could go on. There are hundreds of indicators, more all the time. Themost common one we’ve skipped is the slope of the yield curve: Flat ordownward-sloping yield curves are associated with slower-than-usual future

http://research.stlouisfed.org/fred2/series/PERMIT

http://research.stlouisfed.org/fred2/series/HOUST

http://research.stlouisfed.org/fred2/series/UMCSENT

http://research.stlouisfed.org/fred2/series/NAPM


Figure 11.4: Cross-correlation functions: surveys of economic activity.

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Housing starts

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growth in output. More on this in the Appendix.

11.5 The business-cycle scorecard

Now that we understand how to identify good indicators, how do we putthem to work? The central question here is how to combine the inputs ofmultiple indicators. One way to do that is to summarize them informally,which is what we do here. Another is to use multivariate regression, whichis the next topic, but not one we’ll spend much time on in this course.

The business-cycle scorecard is a summary of what selected indicators tell usabout near-term economic conditions. We’ll use the four monthly indicatorspictured in Figures 11.5 and 11.6. In the first figure, we see the monthlygrowth rate of IP (top panel) and the change in (nonfarm) employment forthe period 1960 to the present. They show similar patterns, with the majorpostwar downturns evident in each. Evidently, employment is procyclical,rising in good times and falling in bad times. Industrial production is a“noisier” series, which is one reason that many analysts prefer employmentas a measure of current economic conditions. The lines show us the meanvalue (the solid line) and plus and minus one standard deviation (the dashedlines). The lines are useful benchmarks for telling how strong the currentvalue of an indicator is relative to past experience.

In the second figure (Figure 11.6), we see similar data for new claims for un-employment insurance and housing starts. New claims are reported weekly;


Figure 11.5: Industrial production and employment.

mean plus 1 s.d.

mean minus 1 s.d.

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1970m1 1975m1 1980m1 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1

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The two panels show, respectively, the annual growth rate of industrial pro-

duction and the year-over-year change in the number of people employed.

the figure is based on the four-week moving average. Remember, they arecountercyclical: they rise when the economy weakens. The second panel ishousing starts. You can see in the figure that housing starts don’t alwaysgo up and down with the economy. In the 2001 recession, housing starts fellonly slightly. In 2008, we made up for that, with housing starts falling totheir lowest point since (at least) 1960. None of that will come as a surpriseto you. These four indicators come from the Federal Reserve (industrialproduction), the Bureau of Labor Statistics (employment, new claims), andthe Bureau of the Census (housing starts). These government agencies arethe primary sources of economic indicators in the US. There are private in-dicators also, but the government indicators are widely used and publiclyavailable.

In the business-cycle scorecard, we rate each pro-cyclical indicator as strongpositive if the current value of the indicator is above the “mean plus onestandard deviation” line, weak positive if it’s between the mean line andthe one above it, weak negative if it’s below the mean line but above the“mean minus one standard deviation” line, and strong negative if it’s belowthe bottom line. For countercyclical indicators we reverse the direction:for example, strong positive means below the “mean minus one standarddeviation” line.


Figure 11.6: New claims and housing starts.

mean plus 1 s.d.

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The two panels show, respectively, new claims for unemployment insurance

and housing starts, two popular indicators of economic conditions.

This is a rough cut, to be sure, but a useful one. It leads to this summaryof economic conditions as of August 2014 based on the four indicators wehave seen so far:

• Industrial production: Growth has recently been close to the mean. As-sessment: weak positive.

• Employment growth: The most recent numbers show steady moderategrowth. Assessment: weak positive.

• New claims: They are the only countercyclical indicator in our list. Theyhave fallen dramatically over the last two years, and are now well belowthe long-run average. Assessment: strong positive.

• Housing starts: They remain low by historical standards, although therehas been improvement since 2009. Assessment: weak negative.

These assessments are collected in Table 11.1. Overall, we see one strongpositive, two weak positives, and one weak negative, a mixed set of signalsthat’s not unusual. A more extensive analysis would use more indicators,decide how much weight to give each one, assess how far into the future theypoint, and so on.


Table 11.1: Business-cycle scorecard in action

Strong Weak Weak StrongIndicator Negative Negative Positive Positive

Industrial production xEmployment xNew Claims xHousing starts x

Summary 0 1 2 1

11.6 Regression-based forecasting

A more formal statistical approach is to include as many indicators as we likein a multivariate regression. We estimate the regression by some appropriatemethod and use it to forecast the future. Here are the steps we might followin constructing a forecast of (say) industrial production k months in thefuture.

The first step is to construct the variable we’re forecasting. Let us say thatwe’re interested in the growth rate of industrial production between nowand k months in the future. You can do what you want, but we computethe (annualized) growth rate this way:

γt,t+k = ln(IP t+k/IP t)× (12/k).

We refer to k (here measured in months) as the forecast horizon. Theadjustment factor “12/k” converts the growth rate to annual units. For aone-year forecast, then, we would set k = 12 and compute the year-on-yeargrowth rate.

The second step is to find some variables you think would be useful inforecasting. The previous section might give you some ideas. There’s a half-step that sneaks in about here, too: what form of the indicator to use. Inmost cases, we use growth rates of the indicators, too, either over one periodor a year, whichever you think works best. But some variables are used as is.In Figure 11.3, for example, the cross-correlation for the unemployment rateis for the rate, period — not its growth rate, change, or other transformation.

Third, you put all the ingredients into a statistical package and run a regres-sion. For example, to forecast IP growth, we would estimate the regression

γt,t+k = a+ bxt + residual,


where xt is the value of the indicator we have chosen. We use a sample ofdata to estimate the parameters a and b. Note well: The growth rate isbetween now (date t) and a future date (t+k), but the indicator is observednow (at t). This is central to the exercise: We use what we know now topredict the future. It’s not kosher to use future variables to predict thefuture because we don’t know the future when we make the forecast (duh!).

Fourth and last: Once we have estimates of the regression parameters (a

and b, say), we use them and the current value(s) of the indicator(s) (x,say) to compute the forecast:

γt,t+k = a+ b xt.

The “hats” remind us that we are using estimates; γt,t+k is our forecastof future growth. There are lots of variants of this approach — you canadd multiple indicators, lags of the indicators (xt−1, xt−2, ...), and even pastvalues of the growth rate of industrial production. We recommend all of theabove.

The result of such an exercise is generally a useful forecast — useful inthe sense that it tells us something about the future. Something, but noteverything! Over periods of a year or two, forecast accuracy is usuallymodest. Even in-sample, the regressions rarely have R2s above 0.25, whichtells us that most of the variation (at least 75 percent) in our forecast variableis unexplained. Some people see a lesson in this: It might be more importantto know how to respond when the unexpected occurs than to have betterforecasts. In practice, both are useful: knowing something about the future,and having backup plans to deal with the inevitable forecasting errors. Itpays to carry an umbrella when the forecast calls for rain.

11.7 Aggregation and prediction markets

There’s another appealing approach to forecasting: Let markets do the work.Most of the best forecasts aggregate information from multiple indicatorsand sources. Indexes of leading indicators do this one way by combiningmultiple indicators to produce an index, which is then used to forecast thefuture. Or we could use multiple indicators in regression-based forecasts, aswe suggested above.

Another approach is to aggregate the forecasts themselves — that is takeseveral forecasts, perhaps based on different indicators, and average them.The business-cycle scorecard is a simple version of this. The so-called “BlueChip” forecast is an average of forecasts generated by experts, and it per-forms better than any single forecaster. Some statistical forecasters do the


same sort of thing on their own. They generate multiple forecasts withmethods like our forecasting regression, and then average them to generatea final aggregate forecast. Again, the aggregate tends to do better than theindividual forecasts.

A related idea is to rely on markets, which aggregate information from thepeople using them. Presidential futures markets, for example, have predictedthe popular vote in the last four elections more accurately than any of themajor polls. In the economic arena, there are a growing number of marketsin which you can trade futures contracts whose payoffs are tied to the valueof specific economic numbers: the consumer price index, the fed funds rate,and so on. These markets are increasingly used as forecasts themselves, withone wrinkle. The simplest interpretation is that the futures price is a marketforecast of the relevant economic number. For example, if we are interestedin the value of an economic number y to be released in 6 months (yt+6, say),we might use its current futures price (ft, say):

ft = Market’s Current Forecast of yt+6.

Experience (and possibly some insight) tells us that we may want to makea correction for the risk of the contract:

ft = Market’s Current Forecast of yt+6 + Risk Premium.

There’s no limit to the amount of sophistication we can bring to bear onthe last term, but for now, you can simply note that we probably want toaddress it in some way. Once you do, markets are an extremely useful sourceof information about the future.

Executive summary

1. Fluctuations in economic activity can be (partially) predicted by a num-ber of indicators.

2. The cross-correlation function is a tool for describing the timing of therelation between two indicators: for example, whether one indicator leadsanother.

3. Markets are useful aggregators of information — and increasingly popularsources of economic forecasts.

Review questions

1. Terminology. Consider economic indicators in general.

http://tippie.uiowa.edu/iem/markets/pres12.html


(a) What is a procyclical indicator? A countercyclical indicator?

(b) Give an example of each.

(c) What is a leading indicator? A lagging indicator?

(d) Give an example of each.

Answer.

(a) A procyclical indicator moves up and down with GDP. A counter-cyclical indicators goes up when GDP moves down. We typicallyidentify this feature with the sign of the correlation.

(b) Most indicators are procyclical : employment, the S&P 500, and soon. The unemployment rate is the classic countercyclical indicator.

(c) A leading indicator is correlated with future GDP growth, a laggingindicator is correlated with past GDP growth.

(d) The stock market is a leading indicator, the unemployment is alagging indicator. We typically identify this feature with the cross-correlation function.

2. Housing starts. We mentioned housing starts as an indicator of futureeconomic activity. In what ways do you think it’s a good indicator? Abad one? (For further information, see the US Census Bureau’s web site.)

Answer. Good: connected to housing, which, as a durable good, shouldbe cyclically sensitive and volatile; available quickly; it leads the cycle (asyou can see from its ccf). Bad: based on a sample, which leads to short-term noise; revised periodically; strong seasonality; possibly misleadingnow that we have a glut of housing to work off.

3. Unemployment. The unemployment rate is widely reported in the press,but professionals rarely use it. Why do you think that is?

Answer. One reason is that the unemployment rate understates thechange in employment in a downturn. Some people who lose jobs leavethe labor force, so they’re not included in the unemployment rate. An-other reason is that the unemployment rate is a lagging indicator. It fallsslowly, well after the economy turns around. Employment (the numberof people actually working) is the preferred indicator for both reasons.

4. Terrorism futures. In 2002, a government agency recommended that weestablish a futures market in terrorist attacks, on the grounds that itwould give us a useful public indicator of their likelihood. The idea waswidely criticized. Do you think it was a good idea or a bad one? Whatwould you need to do to implement it?

Answer. Another case of a good idea thrown out because it soundedbad to politicians. It’s not clear that such attacks are predictable, but ifthey are, we’d expect futures markets to do as well as any other method.

http://www.census.gov/construction/nrc/


To implement the idea, you’d need to define (and possibly quantify) aterrorist event.


There are many sources of leading indicators around the world and almostas many guides to them. Among them:

• The best book we’ve seen on the subject is Bernard Baumohl, The Secretsof Economic Indicators. If you use economic indicators in your job, youshould buy this book.

• The Bloomberg Economic Calendar gives release dates and short sum-maries of a wide range of indicators. Ditto the WSJ, Yahoo, etc.

• The CME has a nice report, “Impact of economic indicators,” on theinformation content of common indicators for futures prices.

Most statistical software packages have one-line commands to compute cross-correlation functions. You can also do it in a spreadsheet, but it’s a lot morecumbersome.

To do more with this topic, you need some knowledge of time series statistics.If you’d like to learn more about forecasting economic and financial variablesspecifically, we recommend “Forecasting Times Series Data,” course STAT-GB.2302, taught in alternate years by Professors Deo and Hurvich, two ofour best statisticians.



Symbol Definition

ccf Cross-correlation functionccf(k) Correlation of (xt, yt−k) at lag kγt,t+k Continuously compounded growth rate from t to t+ kx Estimate of xft Futures price at time t

http://www.amazon.com/The-Secrets-Economic-Indicators-Opportunities/dp/0132932075/

http://www.amazon.com/The-Secrets-Economic-Indicators-Opportunities/dp/0132932075/

http://www.bloomberg.com/markets/ecalendar/index.html

http://www.cmegroup.com/education/featured-reports/impact-of-economic-indicators.html



Variable Source

Industrial production INDPROReal GDP GDPC1S&P 500 SP500Employment PAYEMSUnemployment rate UNRATENew claims IC4WSAHours worked AWHMANBuilding permits PERMITHousing starts HOUSTconsumer sentiment UMCSENTPurchasing managers’ index NAPM10-year Treasury yield GS102-year Treasury yield GS2Federal funds rate FEDFUNDS

To retrieve the data online, add the identifier from the sourcecolumn to http://research.stlouisfed.org/fred2/series/. Forexample, to retrieve nonfarm employment, point your browser tohttp://research.stlouisfed.org/fred2/series/PAYEMS



12Money and Inflation

Tools: The quantity theory; central bank balance sheet; open market op-erations.

Key Words: Price level; inflation; hyperinflation; quantity theory; velocity;fiscal dominance.

Big Ideas:

• Inflation is the growth rate of the price level, which is typically measuredby a price index.

• The quantity theory links the money supply with the price level and out-put. In the long run, an increase in the money supply results in an increasein the price level (inflation).

• Hyperinflation refers to an inflation rate of 100% per year or more. Hy-perinflations follow a standard pattern: government deficits are financedwith money, which produces inflation. We call this fiscal dominance overmonetary policy.

Inflation is the rate of growth of the price level, typically measured by a priceindex. If prices are rising, on average, we have inflation. Milton Friedman,winner of the 1976 Nobel Prize in economics, once said: “Inflation is alwaysand everywhere a monetary phenomenon. To control inflation, you need tocontrol the money supply.” Friedman believed what he said, but he alsoenjoyed thumbing his nose at the popular Keynesian theory of the 1960s, inwhich inflation was the result of excess demand for goods.

151


Was Friedman right? We consider his claim in the context of hyperinflations:episodes of annual inflation exceeding 100 percent per year. Although ex-treme, big inflations are a recurring phenomenon and a wonderful laboratoryfor studying inflation more generally. In these situations (but not necessarilyin others), money growth is present, but it’s invariably connected to gov-ernment deficits. The keys to stopping a big inflation, then, are to balancethe government’s budget and prevent the central bank from expanding themoney supply. The idea that inflationary monetary policy might stem fromfiscal policy is generally referred to as fiscal dominance.

12.1 The quantity theory

Friedman’s claim about inflation is based on a theory that is several centuriesold: the quantity theory of money . Like a lot of good theory, it’s based onan analogy. Think for a moment about the effect of a two-for-one stocksplit on the price of a stock. If it’s now selling for 100, then you’d probablyexpect it to sell for 50 after the split. (This wouldn’t be true if the splitwere a signal of some new information about the firm, but let’s assume it’snot.) The point is that the value of a firm’s total stock of equity shouldn’tdepend on anything as arbitrary as the number of shares.

Now suppose we do the same thing with money. This is unrealistically sim-ple, but makes the point effectively. Suppose that the government replacedevery dollar with two “new dollars,” marked so we could tell the differencebetween old and new notes. Then you’d expect that new dollars would beworth half as much as old dollars. That is, you’d expect prices of goodsand services quoted in new dollars to be twice as high as prices quoted inold dollars. In short, changes in the quantity of money in circulation (the“money supply”) executed in this way will be associated with proportion-ate changes in prices, with no effect on output. Why the latter? Becauseoutput is determined by productivity and inputs, and we wouldn’t expecteither one to be influenced by the number of pieces of paper used to maketransactions.

Of course the world is more complicated than this, and monetary policyconsists of more than just currency exchanges, but some of the same reason-ing applies more generally (we’ll look at some data shortly). The quantitytheory is the result of two ideas: that money is not fundamental (pieces ofpaper don’t change the productivity of the US or Chinese economies), andthat its usefulness is in executing transactions. Let’s start with the latter.In all developed economies, transactions consist of exchanges of goods andservices for money. If we approximate the volume of transactions in an econ-omy by nominal GDP, then we have M = PY , where Y is real GDP and

12. Money and Inflation 153

P is a measure of the price level such as the GDP deflator. This isn’t quiteright yet. A dollar can be used to execute several different transactions in agiven year. To take this into account, we use

MV = PY, (12.1)

where V is the velocity of money: the number of times a dollar is used toexecute transactions in a given year.

At this level of generality, equation (12.1) is a tautology: For any data wecollect on M , P , and Y , we simply choose V to make the equation hold.What gives the equation content is Friedman’s assumption that velocityV is (at least approximately) constant. This implies that increases in Mare associated with proportionate increases in PY . We add one furtherassumption to get Friedman’s connection between money and prices: thatreal GDP is determined by the productivity and inputs of the economy, andis not affected by the amount of money in circulation. We can — and will— change that later, but it seems like a good place to start.

The same theory explains inflation if we express it in growth rates. Aswith growth accounting, we focus on continuously compounded growth rateswhere the growth rate of a variable X is γX = lnXt − lnXt−1. In logs,equation (12.1) and its first difference are:

lnMt + lnVt = lnPt + lnYt

(lnMt − lnMt−1) + (lnVt − lnVt−1) = (lnPt − lnPt−1) + (lnYt − lnYt−1)

γM + γV = π + γY ,

where π = γP is the inflation rate (the rate of growth of the price level). Ifwe assume that velocity is constant,

γM = π + γY , (12.2)

and changes in the growth rate of money are associated with changes inthe growth rate of inflation and output. The second assumption is that thegrowth rate of money does not influence output, so changes in money growthtranslate one-for-one into changes in inflation. That’s Friedman’s argument,which depends on these two assumptions.

12.2 Evidence

It’s not that easy to check the second assumption, but we can check the first(constant velocity) by looking at the components of equation (12.1). If ve-locity is constant, movements in the price level P mirror those in M/Y . We


check this in Figure 12.1, which graphs both variables for the US. (Moneyhere is M2.) The figure suggests that the theory is a reasonable approxima-tion of the data, at least over the last fifty years or so. The two increasinglines (P and M/Y ) show some differences, but their long-run movementsare similar. Overall, velocity has been largely flat, but since the financialcrisis of 2007-09 it has fallen amid record low interest rates. Time will tellwhether or not the change is temporary.

Figure 12.1: The quantity theory in the long run.

M/Y

Price level

Velocity

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ms

1960q1 1980q1 2000q1 2020q1

The short-run evidence for the quantity theory is much weaker. When welook at year-on-year growth rates, as we do in Figure 12.2, we see that veloc-ity has as much short-run volatility as M/Y . As a consequence, movementsin prices are virtually unrelated to movements in money. To put it bluntly,the quantity theory is a poor guide to short-run fluctuations in inflationrates.

12.3 Changing the money supply

Currency is a liability of the government, which can (and does) change thequantity in circulation. To see how this works, it’s helpful to take a stepback and consider the broader issue of government debt. We can divide thegovernment’s debt management into two related pieces. The first piece isthe size of the debt. Measured in units of currency (dollars, say, or pesos),the debt changes over time as the government runs surpluses or deficits.

http://research.stlouisfed.org/fred2/series/M2


Figure 12.2: The quantity theory in the short run.

M/Y

Velocity-5.0

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Mathematically, we might write:

Debtt = Debtt−1 + Deficitt.

This is an example of a government budget constraint, something we’ll seemore of later on. The second piece is the composition of the debt. In prac-tice, governments have many different liabilities, but for the purposes of thisdiscussion, let us say, it has two: government bonds and money (currency).In both theory and practice, these two pieces are typically separate, withthe treasury issuing bonds to cover the entire debt and the monetary au-thority (central bank ) buying back some of these bonds and issuing moneyin return.

Day-to-day monetary policy in most countries consists of what we termopen-market operations: purchases or sales of government debt (bonds). Atany point in time, the treasury’s balance sheet looks something like:

TreasuryAssets Liabilities

Bonds 200

and the central bank’s looks like:

Central bankAssets LiabilitiesBonds 100 Money 100


If it seems strange to treat money as a liability of the central bank (isn’tmoney an asset?), think of it as a bond with the unusual feature that itsnominal interest rate is zero. That’s what it is, which makes it a good dealfor the borrower.

An open-market purchase of bonds results in an increase in bonds held bythe central bank and an equal increase in its monetary liability. For example,a purchase of 20 worth, of bonds would change its balance sheet to:

Central bankAssets LiabilitiesBonds 120 Money 120

The result is an increase in the amount of money in private hands, since theprivate sector (the other side of this transaction) has reduced its holdingsof government bonds and increased its holdings of money. Similarly, anopen-market sale of bonds would reduce the amount of money in privatehands.

The question we’re leading up to is why money growth is so high in countrieswith big inflations. Why does the central bank keep issuing money?

12.4 Big Inflations

If inflation is as easily cured as Friedman suggests (“control the moneysupply”), why do big inflations happen? People who live through suchepisodes describe them as traumatic; they spend an hour or more every dayconverting cash into anything with stable value: real estate, cars, foreignassets. The economy is usually a mess, but whether that is cause or effectis hard to say. But if big inflations are so painful, why do governments letthem happen? The problem, typically, starts with a government deficit. Apolitical impasse makes it nearly impossible to reduce the deficit. Given thegovernment’s budget constraint, it must then issue debt. There is apparentlyno shortage of ready buyers of US debt (ditto other developed countries),but the same can’t be said for every country. If no one will buy its debt,the only remaining option is to finance the deficit with money (read: obligethe central bank to purchase bonds from the treasury). In short, when thegovernment can’t pay its bills in any other way, it pays them with money,which is easy enough to print. The effect of this, of course, is inflation.

The impact here of fiscal policy (government deficits) on inflation is referredto as fiscal dominance, because fiscal policy dominates monetary policy. No-bel Prize-winner Thomas Sargent and his co-author, Neil Wallace, described


a stark version of this. They showed that even a central bank that aims forlow inflation will fail if the government issues debt without end. Think ofthe problem as a version of the time-consistency problem discussed in Chap-ter 6. If everyone knows that the central bank eventually will be compelledto print money to avoid outright default by the government, inflation ex-pectations will rise today despite the central bank’s caution. The key isthat the bank cannot credibly commit to limit future money creation, whileexpectations of the future drive price setting today.

The conventional solution to ending a big inflation has two parts. Thefirst is fiscal discipline: Balance the government budget. The second ismonetary discipline: Separate the central bank from the treasury and tellthe bank that its job is to maintain price stability. Though there are manyfine points — how quickly must the deficit be eliminated? should the IMFsupply short-term financing? — the outlines of the problem and its solutionare clear. Going back to Friedman’s quote: Inflation may be a monetaryphenomenon, but the trouble often starts with fiscal policy and the politicalsituation that led to it. When fiscal imperatives drive monetary policy —like the fiscal dominance in the Sargent and Wallace analysis — inflationeventually follows.

For someone operating an international business, the thing to remember isthat “big inflations” are relatively common. What do you do if you’re hitwith one? You’ll probably find that the most important thing you can dois streamline your cash management. If you can reduce the payment termsfrom (say) 60 days to 30 days, you increase your “real” revenue substantially.You may also find that big inflations lead to policies — such as price controlsand capital controls — that make life more complicated. Finally, you mayfind that your financial statements are highly misleading, since they measureperformance in terms of the local currency, the value of which is changingrapidly. For a US subsidiary, high inflation triggers a change in the rules fortranslating financial entries into dollars for tax and reporting purposes.

12.5 Inflation and interest rates

The interest rates we typically use are nominal: They tell us how muchmoney we get in the future for a given investment of money today. Sinceinflation measures the change in the value of money, it shows up in interestrates. More concretely, we would say that the nominal interest rate equalsthe real interest rate (the interest rate adjusted for inflation) plus expectedinflation:

it = rt + πet . (12.3)


For a given real interest rate r, an increase in expected inflation raises thenominal interest rate one for one.

Here is the deeper explanation behind equation (12.3). Consider a one-yearinterest rate on a Treasury bill. The rate tells us how many dollars (say)we get in one year for a given payment of dollars today. For example, if a12-month treasury bill has a price of $96.15, its annualized yield is the valueof i that solves

96.15 =100

1 + it. (12.4)

In this case, it = 4 percent. Thus, each dollar invested today gives us 1.04dollars in 12 months. We refer to it as the nominal rate of interest —nominal because its refers to payments of currency.

For many purposes, we’d like to know not only the dollar yield, but also howmuch 1.04 dollars will buy when we get it. If we expect the inflation rate tobe 3 percent a year, then we’d guess that three quarters of the interest willbe eaten up by inflation. The investment gains us only about one percentin terms of purchasing power. We refer to the increase in purchasing poweras the real rate of interest — real because it refers to the quantity of realconsumption it finances. That gives us equation (12.3).

We can show this more formally by translating the words into equationsmore carefully. We have just argued that investors are interested not in themoney the bond is a claim to, but in what that money will buy. If by “whatthat money will buy,” we mean the basket of goods used to construct theCPI, we can define the real interest rate r as

(96.15/Pt) =100/Pt+1

1 + rt,

where Pt is the CPI index in year t and Pt+1 is the expected value of thesame index in year t+ 1. What we are doing here is expressing the currentbond price, measured in terms of what it will buy, as the discounted valueof the principal, also measured in terms of what it will buy. Doing a littlealgebra, we find

(1 + rt)(Pt+1/Pt) = 100/96.15.

Then, equation (12.4) tells us that the real and nominal interest rates arerelated by

1 + it = (1 + rt)(1 + πet ),


where (Pt+1−Pt)/Pt is the expected inflation rate between t (now) and t+1(a year from now). Since the product rtπ

et is a small number when expected

inflation is low, it follows that

it ≈ rt + πet , for small values of r and πet ,

where ≈ means “equals approximately.” If we’re careful about timing, wesee that all three variables are comparisons between now and one year fromnow. Inflation is, therefore, typically understood to be expected inflation,since we don’t know what inflation will be when we buy the bond. Inprinciple, we could also take into account the risk inherent in inflation —but we won’t.

Now that we’re done with definitions, we can ask how inflation affects nom-inal interest rates. In principle, either component (the real rate or expectedinflation) can change the nominal interest rate. In practice, we typicallyfind that in periods of high and variable inflation, the inflation componentdominates. This is approximately true of the US, where high-inflation peri-ods (the 1970s and early 1980s) are high-interest-rate periods, too. It’s evenmore evident in countries with very high inflation rates.

12.6 Velocity reconsidered

In very-high-inflation environments, people often find that the inflation rateaccelerates quickly, often far exceeding the rate of money growth. One factorhere is velocity, which typically rises sharply with inflation. Why? Becauseinflation (and nominal interest) is effectively a tax on holding money: Thehigher the tax, the less money you hold. During big inflations, people spendmoney as soon as they get it, because its value falls by the minute. It’scommon, for example, for people to buy groceries and gasoline as soon asthey get their paychecks; if they wait even a day or two, their purchasingpower falls.

If velocity V rises with inflation, then we can reconsider

γM + γV = π + γY . (12.5)

If γY is approximately constant, then an increase in money growth not onlyproduces inflation directly, but its impact is also magnified by the increasein the interest rate, which increases velocity (γV > 0). Similarly, whenhyperinflations are reversed, we often see a larger drop in inflation than inmoney growth, as velocity falls.


Executive summary

1. Over long periods of time, inflation is closely related to money growth.

2. Extremely high rates of inflation are invariably associated with high ratesof money growth.

3. High money growth is often the result of financing large fiscal deficitswith money. The deficits, in turn, often reflect some kind of politicalgridlock.

4. High inflation is typically associated with high interest rates, since in-vestors demand higher yields to compensate for the loss of purchasingpower of the currency.

Review questions

1. Policy rule. Friedman suggested that the Fed might do better to adopta rule in which it kept the growth rate of the money supply constant.

(a) If the growth rate of real GDP is 3 percent, on average, what growthrate of the money supply would deliver average inflation of 2 percent?

(b) What are the strengths and weaknesses of such a policy rule?

Answer.

(a) If velocity is constant, then equation (12.2) gives us a money growthrate of

γM = π + γY = 2 + 3 = 5.

In words: Money growth accommodates inflation and economic growth.

(b) Strengths: predictable, good average inflation performance, avoidmajor policy mistakes. Weakness: no room for policy to respond tocurrent conditions. Compare, for example, policy in the aggregatesupply (AS) and demand model (coming up).

2. Central bank independence. Why do many countries make central banksindependent of the treasury?

Answer. The idea is that monetary policy should focus on good long-termperformance and, to accomplish this, should be immune to short-termpolitical pressure. With respect to hyperinflations, you might argue thatif the government does not have access to money finance, it will be forcedto confront its deficit issues earlier, which is a good thing.


3. Zimbabwe. Zimbabwe ended its hyperinflation by abandoning its cur-rency. Even official transactions were switched to either US dollars orSouth African rand. Does this seem like a good solution? Does it makesense for a country to abandon its currency?

Answer. There’s a long tradition of each country having its own currency,but there’s good reason to think at least some countries would be betteroff using someone else’s. Zimbabwe has shown no ability to manage it’sown currency effectively, so using another sounds like a move in the rightdirection. There are other examples — Panama and Ecuador use the USdollar — and perhaps there should be more.

4. Interest rates and inflation. Go to FRED and find the three-month trea-sury bill rate (TB3MS) and the consumer price index (CPIAUCSL). Ma-nipulate them as needed and graph the nominal interest rate and inflationrate together. What do you see?

Answer. Do it and see!


Wikipedia has a nice article on hyperinflation, including a list of the biggestones of all time. Steve Hanke and Nicholas Krus survey the compete historyof hyperinflation in “World Hyperinflations.” Search: “hanke krus hyperin-flation.” Two really good (but more technical) pieces about specific episodesare Thomas Sargent, “The ends of four big inflations,” and Thomas Sargentand Joseph Zeira, “Israel 1983.”


http://www.cato.org/publications/working-paper/world-hyperinflations

http://www.nber.org/chapters/c11452.pdf

http://www.sciencedirect.com/science/article/pii/S1094202511000147




Symbol Definition

M Money stockV Velocity of moneyP Price levelY Real output or GDPln Natural logγx Continuously compounded growth rate of xπ Inflation (= P )πe Expected Inflationi Nominal interest rater Real interest rate (= i− πe)


Variable Source

Nominal GDP GDPM2 monetary aggregate M2SLM2 velocity M2VConsumer price index CPIAUCSL

To retrieve the data online, add the identifier from the source col-umn to http://research.stlouisfed.org/fred2/series/. For exam-ple, to retrieve nominal GDP, point your browser to http://research.

stlouisfed.org/fred2/series/GDP




13Aggregate Supply and Demand


Key Words: Short- and long-run aggregate supply; sticky wages; aggregatedemand; supply and demand shocks; Keynesian.

Big Ideas:

• The AS/AD model relates output and prices in the short and long runs.The model is composed of (i) an upward-sloping short-run aggregate sup-ply curve, which inherits its shape from sticky wages; (ii) a vertical long-run aggregate supply curve; and (iii) a downward-sloping aggregate de-mand curve.

• Shocks to the aggregate supply and demand curves have different effectson inflation and output.

We’ve seen that economic fluctuations follow regular patterns and that thesepatterns can be used to forecast the future. For some purposes, that’senough. But if we want to make sense of analysts’ discussions of businessconditions, of monetary policy, or of situations that don’t fit historical pat-terns, we need a theoretical framework. The aggregate supply and demandmodel is the analyst’s standard, the implicit model behind most popularmacroeconomic analysis. It’s not the answer to all questions, but it’s a use-ful tool for organizing our thoughts. Think of these notes as the executivesummary; textbooks devote hundreds of pages to the same topic. If you’dlike to go deeper, see the references at the end of this chapter.

We take one common shortcut. In our theory, the variables are real out-put and the price level. In practice, we refer to output growth and inflation.

163


There’s a modest disconnect here between theory and practice, but it’s some-thing that can be worked out. You can thank us later for saving you thetrouble of doing it explicitly.

13.1 Aggregate supply

The standard business-cycle model used by analysts is an adaptation of thesupply and demand diagram. We refer to the curves as aggregate supplyand aggregate demand to emphasize that we’re talking about the wholeeconomy rather than a single market — and to remind ourselves that theanalogy with supply and demand in a single market is imperfect. Figure 13.1is an example. The aggregate supply (AS) curve represents combinationsof output (real GDP, which we denote by Y ) and the price level (an indexP such as the GDP deflator) consistent with the decisions of producers andsellers (“supply”). The aggregate demand (AD) curve represents combina-tions of output and the price level consistent with the decisions of buyers(“demand”).

Here’s how aggregate supply works. We start with the production function,

Y = AKαL1−α, (13.1)

where (as usual) Y is output, A is total factor productivity, K is the stockof physical capital (plant and equipment), L is labor, and α = 1/3.

In the simplest “classical” theory, Y is fixed because nothing on the right-hand side of (13.1) changes in the short run. Although current productivityA and capital K can change over time, we often assume that their currentvalues are set — that is they can’t be changed by current decisions. Capital,for example, takes time to produce: We can increase next year’s capitalstock by investing today, but today’s capital stock is whatever we happento have. Labor L is determined by supply and demand in the labor market,which gives us a level of work that reconciles firms’ demand with individuals’supply. The result is a vertical aggregate supply curve, such as AS∗ in thefigure, in which output does not depend on the price level P .

A vertical aggregate supply curve was the state of the art until the 1930s,when John Maynard Keynes (pronounced “canes”) decided that the Depres-sion demanded a new theory. He and his followers (the “Keynesians”) arguedthat the aggregate supply curve should be upward-sloping. Why? The mostpopular argument is that wages or prices are “sticky”: They do not adjustquickly enough to equate supply and demand for labor or goods. One ver-sion of this story is that wages are sticky downward (that is, wages generallydon’t fall when demand for labor declines). The sticky wage analysis goes

13. Aggregate Supply and Demand 165

Figure 13.1: Aggregate supply and demand.

-YY ∗

6P Z

ZZZZZZZZZZZZZZ AD�

��

ASAS∗

A

B

The horizontal axis is real GDP; the vertical axis is the pricelevel. The lines represent aggregate supply (two versions, ASand AS∗) and demand (AD).

something like this: If the nominal wage W is fixed (i.e., very sticky), thenan increase in the price level reduces the real wage W/P , making labor moreattractive to firms, who hire more workers, which raises output. (That is,we continue to use the labor demand curve.)

The Keynesian sticky wage/price story leads to an aggregate supply curvethat is upward-sloping, since an increase in the price level leads to a lowerreal wage and, therefore, more people hired by firms. We refer to it as theshort-run aggregate supply curve, because wages and prices are not thoughtto be sticky forever. Eventually they adjust, putting us on the verticalaggregate supply curve AS∗, which we refer to as long-run aggregate supply.

That’s what aggregate supply looks like, but what kinds of things make itshift over time? Here’s a list:

• Productivity: An increase in A shifts AS to the right. You can see whyfrom the production function (13.1) — an increase in productivity A raisesoutput Y .

• Capital: ditto an increase in K.

• Price of imported oil: This is a more subtle one, but an increase in theprice of oil works like a negative productivity shock in an oil-importingcountry like the US and shifts AS to the left. Why? Because production


involves energy, as well as capital and labor, as an input. In our measure-ment system, GDP consists only of value added by capital and labor. Ifthe price of oil rises, then a larger fraction of total production is paid tooil producers, leaving less for capital and labor and, therefore, reducingGDP. There’s very little question that this is what happens in practice:An increase in the price of oil leads to larger payments to oil producersand smaller payments to capital and labor. Oil producers benefit; oilconsumers do not.

To simplify matters, we’ll assume that these factors shift both AS and AS∗

left or right by the same amount.

13.2 Aggregate demand

The primary role of the Keynesian aggregate supply curve is to allow demandto influence output; if supply is vertical, then changes in demand affect theprice level, but not output. That’s what we assumed when we discussedthe quantity theory — that changes in the money supply affect prices, butnot output. But if aggregate supply is flatter, shifts in demand affect bothprices and output.

But what is the aggregate demand curve and where does it come from?Recall that aggregate demand refers to the purchase of goods and services.The aggregate demand curve tells us how much demand for output there isat each price level.

The simplest version follows from the quantity theory,

MV = PY, (13.2)

which you might recall from Chapter 12. The aggregate demand curve isthe relation between P and Y for a given supply of money M , determinedpresumably by the monetary authority. For simplicity, we will assume thatvelocity V , is constant. That gives us an inverse relation between P and Y ,as shown in Figure 13.1. Changes in M lead to shifts in AD. If we increaseM , then we need either an increase in output Y or an increase in the pricelevel P to satisfy (13.2), so AD shifts up or to the right.

There’s a more complex version in which monetary policy operates throughthe interest rate. The idea is that an increase in the money supply reducesthe interest rate, which stimulates interest-sensitive components of demand,such as business investment and housing.

Other movements in aggregate demand come from the expenditure com-ponents: demand by consumers (C); firms (I); government (G); and the


rest of the world (NX ). You often read, for example, that high demand byconsumers leads to higher output — more on this shortly. Ditto increasesin government purchases (wars are the biggest examples historically) andinvestment by firms (remember, investment is the most volatile expenditurecomponent). Keynes thought investment fluctuations stemmed, in part,from the “animal spirits” of business people, which you might think of asshifts in investment demand driven by psychological factors.

Let’s summarize. The aggregate demand curve is downward-sloping, reflect-ing the decline in the real money supply as the price level increases. Thefollowing factors (“shocks”) shift the aggregate demand curve to the right:

• An increase in the supply of money.

• An increase in government purchases.

• An increase in consumer demand: For given levels of income, consumersdecide to spend more.

• An increase in investment demand: For given levels of interest rates andoutput, firms decide to invest more (animal spirits).

13.3 Aggregate supply and demand together

Now let’s put supply and demand together. Equilibrium is where supplyand demand cross. The only difference in this respect from the traditionalsupply and demand analysis is that we have two supply curves. The short-run equilibrium is where AD and AS cross. The long-run equilibrium iswhere AD and AS∗ cross.

Here’s how that works. The short-run equilibrium is where aggregate supplyAS and aggregate demand AD cross: the point labeled A in Figure 13.1. Inthis example, the economy’s output is below its long-run value Y ∗, indicatedby AS∗. The reason is that the real wage is too high, leading firms to demandless work than individuals would like to offer at the going real wage.

The long-run equilibrium is where aggregate demand AD crosses long-runaggregate supply AS∗: point B in the figure. How do we get there? Eventu-ally, the real wage adjusts (either W falls or P rises), shifting the AS curvedown, until we get to the point where AD crosses the long-run aggregatesupply.

Let’s put our theory to work:


Figure 13.2: The impact of an increase in the money supply.

-YY ∗

6P Z

ZZZZZZZZZZZZZZ AD

ZZZZZZZZZZZZZZZ AD′�

��

ASAS∗

A

B

Aggregate demand AD shifts right to AD′, moving the short-

run equilibrium from A to B.

What is the impact of an increase in the supply of money? Considera short-run equilibrium at a point like A in Figure 13.2. Could the monetaryauthority do something to raise output to its long-run level? An increase inthe money supply will shift AD to the right, as in the new aggregate demandcurve AD′. If we increase the money supply by the right amount, we canestablish a new equilibrium at B, where output is exactly its long-run value.[We recommend that you work through all these shifts of curves on your ownto make sure you follow the argument.] How was this accomplished? Theincrease in the supply of money increased the price level. Since the nominalwage is fixed, the real wage falls, making labor more attractive to firms andthereby increasing employment and output.

Alternatively, suppose that we’re at the long-run equilibrium. What are theshort- and long-run effects of increasing the money supply? The short-runimpact is to raise prices and output, as we move up the aggregate supplycurve. [You should work this out yourself in a diagram.] But the long-run effect is to increase prices, with no impact on output. Why? Becausemonetary policy doesn’t affect the economy’s long-term ability to produce.That’s what we saw with the quantity theory.

What is the impact of an increase in government purchases? Youmight recognize this as an example of a stimulus program. Suppose thatwe start, as we did above, with output below its long-term value, such aspoint A in Figure 13.2. Then, an increase in government purchases shifts


aggregate demand to the right, as illustrated in the same figure.

What is the impact of an increase in the price of oil? Consideran initial short-run and long-run equilibrium, such as point A in Figure13.3. An increase in the price of oil shifts the aggregate supply curve tothe left. Remember: we shift both supply curves horizontally by the sameamount. The new short-run equilibrium is at point B, where AD and AS

′

cross. Eventually the short-run aggregate supply curve shifts until it crossesAD at AS∗

′, giving us long-run equilibrium at C.

Figure 13.3: The impact of an increase in the price of oil.

-YY ∗Y ∗′

6P Z


��

AS

��

AS′AS∗AS∗′

A

B

C

D

Aggregate supply curves shift left from AS/AS∗ to AS′/AS∗′,

moving the short-run equilibrium from A to B.

Note that this adverse supply shock reduces output but raises the price level.People sometimes refer to this combination as “stagflation,” a term coinedto describe what seemed to be a surprising or implausible outcome. In fact,it’s a natural result of leftward shifts in the aggregate supply curve. Notethat “supply shocks” are inflationary, in the sense that they raise the pricelevel unless something is done to aggregate demand to offset them.

Where do business cycles come from? It’s obvious that we can generateeconomic fluctuations by shifting the aggregate supply and demand curvesaround. Less obvious is what kinds of shifts are most common, or how theylead to the patterns we see in the data. As a rule, shifts in AD move priceand output in the same direction, while shifts in AS move price and outputin opposite directions. By looking at the statistical relation between pricesand output, we can get a sense of whether supply or demand shifts are moreprevalent.


13.4 Beyond supply and demand

This is a nice model, relatively easy to use, and applicable to lots of things.But it’s theory, not the real world. Eliza Doolittle notwithstanding, it’s oftena mistake to fall in love with your own creation. Economists have learnedto be humble; some might say that we have a lot to be humble about.

The aggregate supply and demand framework can be developed further, butit has two weaknesses that are hard to overcome. The first is what we mightterm general equilibrium: Many things affect both supply and demand, so itseems artificial to separate them as we have. The second is dynamics: Theimpact of many shocks depends not only on what happens now, but alsoon what we expect to happen in the future. That’s a hard thing to modelexplicitly, more so in a single diagram.

Consider the interaction of supply and demand. If productivity rises, is thata shift of supply or demand? Obviously it shifts supply: The productionfunction shifts, which directly affects producers. But consumers are alsoproducers. An increase in productivity raises wages, which gives them moreincome, perhaps leading them to consume more. It also raises the demandfor capital goods, since capital is now more productive. Are these shiftsin demand? In the sense that they change consumption and investmentdecisions, the answer is yes. The closer you look, the harder it is to separatesupply from demand.

Another example is the financial crisis. Did it shift supply or demand?Think about it and let us know what you come up with.

Or consider dynamics. One issue is causality. Think about popular com-ments to the effect that consumer demand is driving the economy. A jour-nalist might say: “High consumer demand led to an economic boom.” Thelogic is perfectly consistent with our AS/AD analysis, but is that reallywhat’s going on? If we think about consumption, one of our first thoughtsshould be to think about our future income. If we expect to have muchhigher income in the future (that MBA is really paying off!), we might con-sume more now. But think about what that does to causality. For theeconomy as a whole, has output gone up because we consumed more, or didwe consume more because we expected output to go up? It’s not easy totell the difference between the two mechanisms.

Investment is similar. Firms make investment decisions based on their as-sessment (i.e., guess) of market conditions years down the road. That’s why“institutions” are so important. Good institutions give firms some assurance


that the rules won’t change in ways that make the investment less attrac-tive. With respect to business cycles, we could ask the same question weasked of consumption: Did high investment lead to a booming economy, ordid expectations of a booming economy lead to high investment? If we’reforecasting, we may not care, as long as the two go together. But if we wantto understand what’s going on, we need to address this issue one way orthe other. Fed minutes and analysts’ reports are filled with conjectures overexactly this kind of issue.

A related issue is what we might call context: the set of assumptions peo-ple use to think about the connection between current and future events.Monetary policy is a good example. In most developed countries, centralbanks have worked hard to convince people that if they increase the moneysupply now, it does not signal future increases in the money supply. If itdid, people might immediately demand higher wages, which would lead tohigher prices and inflation. But if they regard a current increase in themoney supply as temporary, they might very well be content with wagesand prices where they are. That’s one of the reasons that monetary policyis different in the US and Argentina: The contexts for understanding cur-rent events are different. It’s also an important practical issue for monetarypolicy: central banks must signal not only their current policies, but theirlikely future policies. That’s exactly what the Fed is struggling with rightnow — how to do that effectively.

Executive summary

1. In the long run, output is determined by the production function: theproductivity of the economy and the behavior and institutions that de-termine investment and employment.

2. In the short run, output may respond to changes in aggregate demand(e.g., the money supply) because of sticky wages or prices or possiblyother market frictions.

3. This is theory, not reality. There’s no substitute for adding some commonsense.

Review questions

1. AS/AD review. Get out a piece of paper and do the following withoutlooking at the text:

(a) Draw the aggregate demand curve on a piece of paper. Why does itslope downward?


(b) Draw the short-run aggregate supply curve on a piece of paper. Whydoes it slope upward?

(c) Draw the long-run aggregate supply curve where the two cross. Whyis it vertical?

(d) What happens in the short run if we increase the money supply? Inthe long run?

Answer. You may refer to Figure 13.2.

(a) The AD curve slopes down because a given quantity of money cansupport a high price level P or high real output Y , but not both.See the quantity theory equation (13.2).

(b) The idea is that a higher price level leads, at a fixed wage rate, tolower real wages, leading firms to hire more workers and expandoutput.

(c) In the long run, wages adjust, and output and employment do notdepend on the price level.

(d) If we increase the money supply, aggregate demand shifts to theright. The immediate impact is to raise output and prices as wemove along the short-run aggregate supply curve. In the long runwages adjust, leading output to revert to its long-run equilibriumlevel and prices to rise.

You might notice that the long-run impact duplicates our analysisof hyperinflation, where money affects prices but not output. Whatwe’ve added is the possibility that monetary policy can affect outputin the short run.

2. Supply or demand? Suppose exports increase sharply. Is this a shift insupply or demand?

Answer. The question is whether this has to do with the production(supply) or purchase (demand) of goods and services. Exports are sales,so it’s a purchase, hence demand. We would approach it the same way weapproached the increase in the money supply in the previous question.

3. France. We’ve seen that the employment ratio is lower in France thanin the US. Should France increase its money supply in an attempt toincrease employment and output?

Answer. Good question, but the answer is no: One suspects that thelevel of employment associated with the long-run aggregate supply curveis lower than markets would produce on their own.

4. Causality. Do increases in consumption cause increases in output, or theother way around? That is, could the correlation between consumption


and output be because high output leads consumers to spend more, ratherthan the reverse?

Answer. We observe data, not causality, and we may not be able to dis-tinguish between alternative causal interpretations of the same events.That’s what makes economic analysis so much fun. In some cases, wemight be able to tell the difference, and these cases might lead to moregeneral insights. For example, winning the lottery generates an increasein consumption, and we can say confidently that the causality runs fromhigher income to higher consumption. Why? Because the reverse argu-ment is absurd: High consumption didn’t cause the person to win thelottery. In most cases, however, we can have multiple plausible causalinterpretations of events, and there’s not much we can do about it.


Similar material is covered in greater depth in most macroeconomics text-books.




Symbol Definition

Y Real output (=real GDP)A Total factor productivity (TFP)K stock of physical capital (plant and equipment)L quantity of labor (number of people employed)α Exponent of K in Cobb-Douglas production function

(= capital share of income)P Price levelY ∗ Equilibrium (or potential) outputAS Short-run aggregate supply (AS)AS∗ long-run aggregate supply (AS)AD aggregate demand (AD)AD′ aggregate demand (AD) after a shockAS′ aggregate supply (AS) after a shockM Money stockV Velocity of moneyC Private consumptionI Private investment (residential and business investment)G Government purchases of goods and services (not transfers)X ExportsM ImportsNX Net exports (= X −M)

14Policy in the AS/AD model


Key Words: Policy objectives; potential output; output gap.

Big Ideas:

• The objectives of monetary policy are generally thought to be (i) stableprices and (ii) output near its long-run equilibrium level.

• A direct consequence is that monetary policy should respond differentlyto demand and supply shocks. As a general rule, policy should resist/offsetchanges in output triggered by shifts in demand and accommodate/reinforcechanges triggered by shifts in supply.

• We can identify supply or demand shocks from whether output and pricesmove together or in opposite directions.

We’ve seen that aggregate demand and supply can shift on their own or,sometimes, as a result of changes in policy, including monetary policy. Butwhat policy changes are called for? Should we always shift the aggregatedemand curve to maintain low inflation? High output? Are these two ob-jectives in conflict? The short answer is that we should respond differentlyto changes in supply and demand. A somewhat longer answer follows.

14.1 Objectives of policy

The traditional guide to economic policy is the invisible hand. If marketswork well, then we simply leave them to do their job. If not, we may act to

175


facilitate their operation. In the aggregate demand and supply framework,the idea is that the long-run aggregate supply curve is where the uninhibitedoperation of markets would lead us. In the short run, sticky wages (orother market imperfections) may delay the adjustment, but that’s where theinvisible hand ultimately would direct us. One consequence is that there’sno compelling reason to change aggregate demand to increase output beyondits long-run equilibrium value. We might be able to do it, but it won’t makeus better off. In a sense, we will have tricked people into working morethan they want, typically by reducing their real wages through unexpectedinflation.

The first objective of policy, then, is to get output as near as possible tothe level associated with the long-run aggregate supply curve AS∗. Thisis important enough a concept that people have given it lots of names:potential output, full employment output, and so on. We’ll call it potentialoutput, with the understanding that it’s the long-run equilibrium, not anupper bound. The output gap is a related concept: the difference betweenactual and potential output. In practice, potential output is a little slippery,because the long-run aggregate supply curve isn’t something we observe.We have a variety of ways of estimating potential output, ranging fromthe complex to the pragmatic (a smooth trend line drawn through actualoutput). We give some examples (and links) at the end of the chapter.

The second objective of policy is price stability. That’s not an obviousimplication of the invisible hand, but experience has taught us that low and(especially) stable rates of inflation are associated with good macroeconomicperformance. You might ask whether we’d be better off with no inflation,low inflation (say, two or three percent a year), or even modest deflation (yes,there are theoretical arguments for that). However, experience suggests thatit doesn’t matter too much. Any stable target is better than the high andvariable inflation that the US and many other countries experienced in the1970s.

14.2 Policy responses to supply and demand shocks

With potential output and stable prices as our objectives, how should policyrespond to changes in aggregate supply or demand? Curiously, the answerdepends on whether we face supply shocks or demand shocks.

How should we respond to demand shocks? Consider a negative demandshock, illustrated by Figure 14.1. The long-run equilibrium is point A,where aggregate supply AS∗ and aggregate demand AD cross. Suppose thatconsumer pessimism shifts the aggregate demand curve to AD′, leaving us

14. Policy in the AS/AD model 177

Figure 14.1: The impact of an adverse demand shock.

-YY ∗

6P Z

ZZZZZZZZZZZZZZ AD′

ZZZZZZZZZZZZZZZ AD�

��

ASAS∗

B

A

Aggregate demand AD shifts left to AD′, moving the short-run

equilibrium from A to B.

at point B. What should we do? If we do nothing, we fail on both of ourobjectives because output is below potential and prices have fallen. Theappropriate policy, then, is to shift the demand curve back to AD, perhapsby expanding the money supply.

That’s a general rule: Policy should offset demand shocks. In this case,there is no conflict between our two goals of hitting potential output andmaintaining stable prices. The policy lesson: We should resist or offsetdemand shocks.

How should we respond to supply shocks? Consider the situation depictedin Figure 14.2: an adverse supply shock that moves us from A to B. Shouldpolicy try to offset the decline in output? If we follow our logic, the answeris no; we want to move output as close to the long-run aggregate supplycurve AS∗′ as possible. We do this by moving the aggregate demand curveleft (left!) until it intersects both aggregate supply curves at point D. Atthis point, the price level is the same as it was at A, so we have deliveredstable prices. Output has fallen more than if we had not acted, but that’swhat the invisible hand suggests. The policy lesson: We should acquiesceto or accommodate supply shocks.

The basic lesson, then, is that we want to react differently to changes inoutput that result from supply and demand shocks. We should resist de-mand shocks and accommodate supply shocks. The difficulty, in practice,


Figure 14.2: The impact of an increase in the price of oil.

-YY ∗Y ∗′

6P Z


��

AS

��

AS′AS∗AS∗′

A

B

C

D

Aggregate supply curves shift left from AS/AS∗ to AS′/AS∗′,

moving the short-run equilibrium from A to B.

is knowing which is which. If we guess wrong, we can make things worse,perhaps a lot worse.

By some interpretations, the Fed made exactly this mistake in the 1970s.With output falling and inflation rising, the Fed increased the money supplyto keep output up. With hindsight, the OPEC oil price increase is under-stood to be an adverse supply shock. It reduced output, but there was littlewe could do about it. When we increased the money supply, the conse-quence was that low output was accompanied by even higher inflation thanbefore. Having failed to understand the problem, we decided to give it aname: stagflation.

Executive summary

1. We typically think of the goals of macroeconomic policy as keeping infla-tion low and output near the long-run supply curve.

2. As a general rule, policy should resist changes in output triggered byshifts in demand and accommodate/acquiesce to changes triggered byshifts in supply.


Review questions

1. Consider the situation in Figure 14.1, where an adverse demand shockmoves us from A to B.

(a) What is your welfare analysis of the change? In what ways is Bbetter than A? Worse?

(b) How would your answer change if AD shifted to the right, ratherthan the left?

Answer.

(a) Recall the objectives of policy: (i) stable prices and (ii) output atits long-run equilibrium value Y ∗. In this case prices fall, so we failon (i), and output moves away from Y ∗, so we fail on (ii).

(b) In this case output and prices both rise, but both are bad from awelfare point of view. Note specifically that it’s not true that moreoutput is better.

2. Current economic conditions.

(a) What have inflation and GDP growth been over the past year?

(b) Would you say demand has shifted or supply relative to the yearbefore?

(c) Using this information and anything else you think is appropriate,where is the economy relative to the long-run equilibrium level ofoutput Y ∗?

Answer.

(a,b) The idea is to look at the numbers and decide whether we seem to beexperiencing a shift in supply or demand — or perhaps neither. Ifinflation and output growth have moved together, we’d say demand.If they’ve moved in opposite directions, we’d say supply.

(c) Good question. What would you suggest?

3. Stimulus in China. In 2009, China responded to the financial crisis by im-plementing a massive program of government spending on infrastructure.Your mission is to outline the argument for or against such a programusing the aggregate supply and demand (AS/AD) framework.

(a) Over the last year, output growth and inflation have both fallen inChina. Would you say this comes from a shift in supply or demand?Illustrate your answer with the appropriate diagram.

(b) Describe the impact of a large increase in government spending oninfrastructure projects. What is the likely impact on output? Oninflation?


(c) What are the traditional goals of macroeconomic policy, expressed interms of aggregate supply and demand? Does the Chinese spendingprogram move them closer to these goals?

Answer.

(a) Shifts in demand move output and prices in the same direction,shifts in supply move them in opposite directions. (By longstandingtradition, we interpret output as output growth and prices and in-flation.) Since they both fell, we would interpret this as a shift leftin demand.

(b) This is a purchase of goods; therefore, it affects demand. A shiftright in demand increases both output growth and inflation.

(c) The goals are (i) output equal to the long-run aggregate supplycurve AS∗ and (ii) stable prices. The answer depends where youstart: Are we to the left of AS∗ prior to the stimulus? If so, thenthe stimulus program moves output in the right direction. Dittowith inflation: If we start with stable prices, the stimulus generatesinflation.

4. Aggregate implications of employer-provided health insurance. By anaccident of history, health insurance in the US is generally provided byemployers. Suppose a sharp rise in healthcare costs leads firms to hirefewer workers.

(a) How would you represent this in an aggregate supply and demanddiagram? Which curve shifts? In which direction?

(b) What is the new short-run equilibrium? Long-run equilibrium?What happens to inflation and output?

(c) How should the central bank respond? Be specific about its goalsand how it would accomplish them.

Answer.

(a) Since we’re talking about firms and production, this must involvethe supply side of the model. We shift AS and AS∗ to the left, bothby the same amount. See the figure below.

(b) We started at A. After the shift, we move to a new short-run equi-librium at B, where the new AS crosses AD. Evidently output fallsand prices rise.

Eventually we move to a new long-run equilibrium at C, where ADcrosses the new AS∗. At this point, output has fallen more andprices have risen more.


-YY ∗Y ∗′

6P Z


��

AS

��

AS′AS∗AS∗′

A

B

C

D

(c) The central bank has two goals: stable prices and output at itslong-run equilibrium. Here we’ve moved from A to C. We’re ok at Con the second goal: output fell, but that’s the long-run equilibriumso there’s nothing monetary policy can do about that. (We couldconsider other policies, but they’re not the job of the central bank.)

Where C is bad is with respect to price stability: prices are higher.So the central bank could shift AD to the left, giving us the samelong-run output but lower prices. The central bank would accom-plish this by reducing the money supply, which it might do by tar-geting a higher interest rate.

5. The supply and demand of Abenomics. Shinzo Abe was elected PrimeMinister of Japan in December 2012 after two decades of slow growth andfalling prices. He pledged dramatic policy changes to revive the Japaneseeconomy, dubbed the “three arrows” of “Abenomics.” We consult theEconomist Intelligence Unit for specifics:

• Fiscal stimulus. A sizeable economic stimulus package was passed byparliament in February 2013, and a smaller one in October.

• Monetary stimulus. A plan to double Japan’s money supply withintwo years was implemented in April 2013 to help to achieve the Bankof Japan’s target of 2% inflation.

• Structural reform. This is less clearly articulated, but some observershope for a range of micro-based reforms, including loosening product-market regulations that reduce productivity, tightening corporate re-quirements for funding pensions, creating a more flexible labor market,and reducing subsidies to an inefficient agricultural sector.

Your mission is to explore the impact of the three arrows using the ag-gregate supply and demand framework.


(a) Explain, for each “arrow,” whether it affects supply or demand.Which way does each one shift the appropriate curve(s)?

(b) Compare the short- and long-term impact on output of the threepolicies. Which are likely to have the greatest impact in the shortterm? In the long term?

Answer.

(a) We have:

• Fiscal stimulus. This shifts aggregate demand to the right.

• Monetary stimulus. Same.

• Structural reform. This shifts both aggregate supply curves to theright.

(b) Fiscal and monetary stimulus raise output in the short run. Theyhave no long-run impact on output.

Structural reform is likely the most important of the arrows for thelong-term performance of the Japanese economy. It should raiseoutput long term, in large part by increasing productivity, but short-term transition issues could go the other way. It’s also the arrowthat’s been executed least aggressively.


The measurement of potential output has generated some interesting debate.The bottom line, in our view, is that there’s usually some question wherethe long-run aggregate supply curve is. Here is a range of opinion on thesubject:

• The Congressional Budget Office (CBO) reviews a number of approaches.Search: “cbo potential output.”

• Former Fed Governor Frederic Mishkin’s speech, “Estimating potentialoutput,” is another good overview. Search: “mishkin potential output.”

• The Kansas City Fed’s 2005 Jackson Hole Symposium has an interest-ing exchange between Robert Hall and Greg Mankiw. Hall argues thatpotential output may very well not be smooth, which would contradictmost measures of it. As a practical matter, this would change our viewof monetary policy dramatically since many of the movements we see inGDP would be the result of the invisible hand and, therefore, not some-thing for policymakers to resist. Mankiw says maybe, maybe not. Search:“Jackson Hole Symposium 2005.”




Symbol Definition

Y Real output (=real GDP)Y ∗ Equilibrium (or potential) outputY ∗′ New equilibrium (or potential) outputAS Short-run aggregate supplyAS∗ Long-run aggregate supplyAD Aggregate demandAD′ Aggregate demand after a shockAS′ Aggregate supply after a shock


Variable Source

NBER recession indicator USRECMCBO real potential GDP GDPPOTOil Price (WTI) OILPRICE

To retrieve the data online, add the identifier from the sourcecolumn to http://research.stlouisfed.org/fred2/series/.For example, to retrieve oil prices, point your browser to http:

//research.stlouisfed.org/fred2/series/OILPRICE


http://research.stlouisfed.org/fred2/series/OILPRICE

http://research.stlouisfed.org/fred2/series/OILPRICE


15Money and Interest Rates

Tools: Open market operations; central bank balance sheet; Taylor rule.

Key Words: Real interest rate; nominal interest rate; expected inflation;real money balances; inflation targeting; interest-rate rules; rules vs. discre-tion; zero lower bound; quantitative easing; credit easing; policy durationcommitment.

Big Ideas:

• In conventional practice, central banks use open market operations tomanage interest rates. These policy actions are equivalent to managingthe money supply directly.

• The Taylor rule provides a guide to how central banks manage their targetinterest rates in response to data on inflation and (real) GDP growth.

• When interest rates are at or near zero, a central bank can resort to un-conventional monetary policy, including quantitative easing, credit easing,and policy-duration commitments. These policies have been in widespreaduse since 2008.

Where do interest rates come from? We doubt this was your first questionwhen you were growing up, but you probably have an opinion about it now.Most people say they’re set by the Fed — or the appropriate central bankif you’re in another country. There’s some truth to that, but it can’t bethat simple. We had interest rates before the Fed was established, and, ifanything, they varied more then than now. It’s probably better to say thatthe Fed “manages” interest rates — that is they vary the supply of moneyto set the market interest rate they think is appropriate, consistent with

185


market conditions. Market interest rates reflect, after all, the behavior ofprivate borrowers and lenders, as well as the Fed.

We outline how this works, starting with a review of interest rates (thereare lots of them) and moving on to monetary policy as practiced in mostdeveloped countries these days. Along the way, we show how you wouldexpect new information about inflation or economic growth to affect interestrates.

15.1 Interest rates

Here’s a quick review of interest rates: real and nominal, short and long,risk-free and risky.

Real and nominal. It may not strike you at first, but interest rates haveunits. The interest rates we’re used to are reported in currency units: A one-period bond pays currency later in return for currency now. That’s one of thereasons why interest rates differ around the world: If countries have differentcurrencies, their interest rates are measured in different units. Since they’remeasured in currency units, we refer to them as nominal interest rates, justas GDP measured in currency units is referred to as nominal GDP.

It’s traditional, as we saw in Chapter 12, to decompose a nominal interestrate i into a real interest rate r and expected inflation πe:

i = r + πe. (15.1)

The real interest rate “corrects” the nominal rate for the loss of purchasingpower reflected in the inflation rate. In words: A nominal interest rate offive percent delivers greater purchasing power in a year if the inflation rateis two percent than if it is five percent.

Short and long. bonds differ, of course, by maturity: that’s the ideabehind the “term structure of interest rates,” a popular finance topic. If weconsider a zero-coupon bond of maturity m years, the price and (nominal)interest rate or yield are related by

qm = 100/(1 + im)m.

The interest rate has been annualized — that’s what the exponent does —but it applies to a bond whose maturity can be something besides one year.

Interest rates on long bonds often differ from those on short bonds. Longrates are higher than short rates, on average, but not always. We commonly

15. Money and Interest Rates 187

attribute the difference to two factors. The first is expected differences ininterest rates over the life of the bond: If we expect short-term interest ratesto rise over the life of the bond, then its interest rate should be higher asa result. The second is risk. Long bonds have greater exposure to the riskof changing interest rates. Their price and yield , therefore, incorporateadjustments for this risk. We can express this in an equation as

im = Expected Future Short Rates + Risk Premium.

Long-term interest rates have a similar distinction between real and nominal.The equation is the same with the appropriate maturities noted:

im = rm + πem.

For example, the expected inflation rate in this case is the one that appliesto the period from now until m years from now.

Credit risk. There’s another source of risk that comes up later in thecourse: the possibility that the borrower defaults. We tend to ignore thatin the US Treasury market, although credit default swaps now price insome such risk. With bonds issued by banks, corporations, and foreign“sovereigns” (governments), the risk can be substantial. We might see, forexample, that interest rates on Argentine or Greek government bonds areseveral hundred basis points above US Treasuries of similar maturity. (Abasis point is one hundredth of a percent.)

15.2 Changing the money supply (review)

We’ll come back to interest rates shortly. But before we do, we considermonetary policy, which plays a central role in their short-term movements.central banks control the quantity of currency in circulation (money, for ourpurposes). We show here how that works, then move on in later sections todescribe how they use their control over money to influence interest rates.Our analysis of the central bank’s control of the money supply involves thebalance sheets of the treasury, the central bank, and individuals and firms.You’ve seen this before, but it’s important enough to run through again.We’ll see it again when we look at fixed exchange rates.

Day-to-day monetary policy in most countries consists of what we term open-market operations: purchases or sales by the central bank of governmentsecurities (bonds ). At any point in time, the treasury’s balance sheet lookssomething like this:


TreasuryAssets Liabilities

bonds 200

The central bank’s looks like this:

Central bankAssets Liabilitiesbonds 100 Money 100

And the private sector’s looks like this:

Private sectorAssets LiabilitiesMoney 100bonds 100Other 500

If it seems strange to treat money as a liability of the central bank , think ofit as a bond with the unusual feature that its nominal interest rate is zero.That’s what it is, which makes it a good deal for the borrower.

An open-market purchase of bonds results in an increase in bonds held bythe central bank and an equal increase in its monetary liability. The privatesector does the opposite; it sells bonds to the central bank, reducing itsholdings of bonds and increasing its holdings of money (currency). Forexample, a central bank purchase of 20 dollars worth of bonds would changethe balance sheets to

Central bankAssets Liabilitiesbonds 120 Money 120

Private sectorAssets LiabilitiesMoney 120bonds 80Other 500


Note that this doesn’t change anyone’s net worth; it’s a portfolio shift,which changes only the composition of assets and liabilities. The result isan increase in the amount of money in private hands since the private sector(the other side of this transaction) has reduced its holdings of governmentbonds and increased its holdings of money. Similarly, an open-market saleof bonds would reduce the amount of money in private hands.

15.3 Managing the interest rate

Typically, we describe monetary policy in terms of managing the short-terminterest rate, which is different from what we’ve described before (namely,controlling the money supply). How does managing the money supply relateto managing the short-term interest rate? Let’s work through the impact ofa change in the supply of money in a simple model.

This is essentially a supply and demand exercise, and the first step is todescribe the demand for money. Consider a modified version of the quantitytheory:

Mt/Pt = Yt/V (it). (15.2)

Here (as before), M is the supply of money (think currency), P is the pricelevel (think price index), Y is real output (real GDP), and V (it) is velocity.We refer to the M/P as real balances: the real value of money issued by thecentral bank and held by the public.

Our key innovation here is allow velocity to increase with the nominal in-terest rate. When the nominal interest rate is high, we will assume thatvelocity is high, and vice versa. As a result, real money balances (M/P )decline when the nominal interest rate rises. We noted the same thing inChapter 12, where we noted that at high inflation rates people did anythingthey could to avoid money, thereby raising its velocity. They same rationaleapplies in less extreme settings: when the nominal interest rate is high, peo-ple shift their portfolios from non-interest-bearing money to interest-bearingassets.

In Figure 15.1 we plot supply and demand curves for money with the nominalinterest rate i on the y-axis and real money balances M/P on the x-axis. Thedownward-sloping line is the demand for real balances. Its slope illustratesthe relationship between real balances and the nominal interest rate: Asthe nominal interest rate rises, the quantity of money demanded falls. Thevertical line is the supply of real balances. At a given value of P , this lineis vertical because supply is determined by the central bank.


We now have a model of the supply and demand for real balances and canexplore the relation between the supply of money and the nominal interestrate.

Figure 15.1: Supply and demand for money.

-M/P

6i Z

ZZZZZZZZZZZZZZ Y/V (demand)

M/P M ′/P (supply)

A

B

The very short-run impact of an increase in the money sup-

ply is a shift right in the vertical supply curve (M/P ) and a

movement down the demand curve (Y/V ) from A to B.

What happens if the central bank increases the supply of moneyM? There are two outcomes, one in the long run and one in the short run. Inthe long run, the price level increases proportionally with the money supply,and the supply curve stays in the same place and nothing changes. That’sthe logic of the quantity theory taken literally: Any increase in money (inthe long run) results in an increase in prices.

In the short run, the results differ. In the short run, we might guess thatproduction plans won’t change (Y is fixed), and we generally think thatprices won’t change either (P is fixed). Then the money-supply curve shiftsout and the interest rate falls. In the figure, we move from point A to pointB. In words: By increasing the supply of money, the central bank drivesdown the interest rate.

The key point here is that we can think of changes in the interest rate asreflecting changes in the money supply. Put this way, there’s little differencebetween changing the money supply and changing the interest rate.

One last thought: Context matters here. If the context is relatively stableprices, changes in the money supply affect the interest rate as described. But


if an increase in the money supply is interpreted as a sign that the centralbank is abandoning price stability, then we could see an increase in thesupply of money raise the interest rate rather than lower it. That’s why youhear central bankers talk about “anchoring expectations” and “maintainingcredibility” for stable prices. More on that shortly.

15.4 Goals of monetary policy

If the tools of monetary policy are the money supply and the short-terminterest rate, what is the goal? Should central banks focus on inflation,growth, or some combination? This, in turn, raises the question of whatthey’re capable of doing. There is clear evidence that monetary policy affectsinflation, at least over periods of several years. Persistent high inflation isinvariably associated with high rates of money growth. There is also clearevidence that countries with high and variable inflation rates have poormacroeconomic performance, although the cause and effect are less clear. Ishigh inflation the cause of poor economic performance, or the result?

With these facts in mind, most countries charge their central banks withproducing stable and predictable prices. In practice, this is typically un-derstood to mean a stable inflation rate of about 2 percent a year. Manyadvanced economies have also made their central banks independent — inthe sense that they can set their policy instrument (usually an interest rate)without being overridden by a legislature or a government for short-runpolitical reasons. (Argentina did this, too, but it didn’t last very long.)

Why have so many countries granted their central banks such “instru-ment independence?” One reason is that it helps overcome a classic time-consistency problem. If people expect a government with a short time hori-zon to set monetary policy, they would expect it to stimulate the economynow even if that spells high inflation later. But if countries appoint con-servative central bankers, they can — in theory, at least — reduce inflationwithout loss of output. When an independent monetary authority can com-mit credibly to keep inflation low, it lowers inflation expectations today andimproves both inflation and output performance.

In the US, the Federal Reserve Act asks the Fed “to promote the goalsof maximum employment, stable prices, and moderate long-term interestrates.” This is, to be sure, the usual political mush — the Fed should accom-plish “all of the above.” The term “maximum employment” is interpretedto mean that the Fed should act to reduce the magnitude and duration offluctuations in output and employment. What role does monetary policyplay in these fluctuations? In the long run, expert opinion is that the im-pact is close to zero; the long-term growth rate of the economy depends on


its productivity and institutions, not on its monetary policy. But in theshort run, expansionary monetary policy (high money growth, low interestrate) probably has a modest positive effect on employment and output. Theconnection is fragile, in the sense that too much monetary expansion seemsto lead not to higher output but to high inflation, higher interest rates, and,perhaps, lower output. Most experts suggest, therefore, that central banks(including the Fed) should emphasize price stability and give secondary im-portance to output and employment.

One of the arguments in favor of price stability is that our attempts to domore have been notably unsuccessful. Ben Bernanke put it this way in a2003 speech at NYU (“Constrained discretion”):

The early 1960s [were] a period of what now appears to havebeen substantial over-optimism about the ability of [monetary]policymakers to ‘fine-tune’ the economy. Contrary to the expec-tation of that era’s economists and policymakers, the subsequenttwo decades were characterized not by an efficiently managed,smoothly running economic machine but by high and variableinflation and an unstable real economy, culminating in the deep1981-82 recession. Although a number of factors contributedto the poor economic performance of this period, I think mosteconomists would agree that the deficiencies of ... monetary pol-icy — including over-optimism about the ability of policy tofine-tune the economy ... played a central role.

Another way to put this: Economists should be humble about what we canaccomplish. (And to paraphrase Winston Churchill, we have a lot to behumble about!)

The focus on price stability is often expressed as a desire for predictability.Firms, investors, and workers all need to have a clear picture of future infla-tion — hence, future monetary policy — since the consequences of currentdecisions depend on it. Built into this statement is a belief that many suchdecisions — prices of bonds, wages and salaries, long-term supply contracts— are expressed in units of currency, whose future value depends on policy.Therefore, it’s helpful for policy to be predictable, so that these decisions canbe made according to their economic merits rather than on guesses of futurepolicy. As Bernanke suggests, the unpredictability of policy in the 1970s wasa factor in the poor macroeconomic performance of that decade. Big infla-tions are an extreme example, in which even day-to-day price changes arenot only large, they’re wildly uncertain. In such conditions, capital marketstypically either disappear or shift to another currency.

http://www.federalreserve.gov/boarddocs/Speeches/2003/20030203/default.htm


With these ideas in mind, many central banks now follow procedures thatfocus on price stability (so that people can make long-term decisions) andtransparency (so that their actions are well understood). In the industrialworld, targeting inflation over the medium term (say, over several years) hasbecome common. The Federal Reserve announced a quantitative inflationgoal (of 2 percent) for the first time in 2012. In developing countries, fixedexchange rates are a common device in which a currency is tied to one thatis thought to be more predictable. Most commonly, there has been a movetoward interest-rate rules that connect (at least approximately) interest ratesset by central banks with inflation and (possibly) output.

15.5 The Taylor rule: the bond trader’s guide

One way to make monetary policy predictable and transparent is to followa rule. The rule tells us how policy will be set, at least approximately,both now and in the future, which makes policy more predictable to marketparticipants, including bond traders.

As we saw in previous chapters, concerns about time consistency tend to fa-vor rules over discretion in setting economic policy. In the case of monetarypolicy, a well-designed rule can help anchor inflation expectations and stabi-lize economic activity. It does so by limiting the scope for future policymak-ers to renege on their commitment to low inflation in return for politicallypopular short-term output gains.

The rules vs. discretion debate has a long history, and a number of monetarypolicy have been proposed over the years. One of the most famous is MiltonFriedman’s k-percent rule, which called for the central bank to increasethe supply of money at a constant rate of k-percent. Subsequent researchsuggests that a “feedback rule” which responds to economic conditions willbe more effective in stabilizing inflation and economic growth over businesscycles. In addition, most research — and virtually all central bank practice— focuses on rules for setting the policy interest rate, rather than the supplyof money.

Of these interest-rate feedback rules, the most famous and widely used isthe Taylor rule. John Taylor suggested in 1993 that an interest-rate rulewould provide a relatively simple summary of monetary policy in manycountries. It’s a guideline really, not a rule, but it nevertheless goes by thename “Taylor rule.” It consists of the following equation:

it = r∗ + πt + a1(πt − π∗) + a2(yt − y∗t ), (15.3)

where it is the short-term nominal interest rate; r∗ is a “normal” or long-term average real interest rate; πt is the inflation rate; π∗ is the target


inflation rate; yt is (the logarithm of) real output; and y∗t is the “normal”(sometimes called “potential”) level of output (also in logarithms). Theparameters a1, a2 indicate the sensitivity of the interest rate to inflationand output.

Let’s walk through equation (15.3) piece by piece, as applied in the US:

• Nominal interest rate i. Standard practice in the US is to use the“fed funds rate.” In the US, commercial banks and other “depositoryinstitutions” have accounts (deposits) at the Federal Reserve that arereferred to as fed funds. They trade these deposits among themselvesin an overnight fed funds market. The Fed currently indicates its policystance by setting an explicit target for the interest rate on these tradesand performs open-market operations to bring the market rate close tothe target. This rate anchors the very short end of the yield curve.

• Normal real interest rate r∗. Experience suggests that the real fedfunds rate (nominal rate minus inflation) has averaged about two percentover the last two decades, but it moves around over time, both over longperiods of time (real interest rates were unusually high in the 1980s andlow in the 2000s) and over the business cycle. Most people simply setr∗ = 2%, but members of the FOMC that determine the policy ratetarget have lowered their estimates of r∗ into the 1.5–2 percent range.The first component of the target fed funds rate is, thus, the target realrate (two percent) plus the current inflation rate, thus giving us a nominalinterest rate target.

• Inflation deviation (π − π∗). The next term is a reaction to the dif-ference between current inflation (π) and the target (π∗). If the targetis two percent and actual inflation is three percent, then we increase thenominal fed funds rate by a1 percent. Typically a1 > 0, meaning that weincrease the interest rate in response to above-target inflation. Why? Be-cause higher interest rates are associated with slower money growth and,therefore, (eventually) lower inflation. Larger values of a1 indicate moreaggressive reactions to inflation. Since inflation enters equation (15.3)both directly and as part of this term, any increase in inflation leads toa greater increase in the nominal interest rate. This “overreaction” isintended to stabilize the inflation rate.

• Output deviation (y − y∗). The final term is a reaction of the interestrate to deviations of output from its normal or potential level. Somepeople use a smooth trend for y∗ or a measure of potential output. (Youmay recall the discussion of Chapter 14.) If we think of the world as theAS/AD model, then potential output is what the economy would generateif wages and prices weren’t sticky — whatever that is! The Fed’s goal,


in this case, is to offset the impact of those frictions on output. Thepractical difficulty is distinguishing increases in y from increases in y∗.One approach is to use the difference in the year-on-year growth ratefrom its mean. This is easier to measure, but has the same issue: it’snot obvious that our measure (the mean growth rate) is the same as thelong-run equilibrium.

• Parameters (a1, a2). Taylor suggested a1 = a2 = 1/2, giving equalweight to inflation and output deviations. Some recent studies of actualcentral bank behavior find larger values of a1 and smaller values of a2— say a1 = 0.75 and a2 = 0.25. By some interpretations, the Europeancentral bank (ECB) places greater weight than the Fed on inflation andless weight on output.

That’s the rule. The bond traders’ perspective is that it’s a reasonable guideto how short-term interest rates respond to data releases, as bond tradersrespond to how they see monetary policy reacting to new information abouteconomic conditions. If a high inflation number comes out, the interest rategoes up. Why? Because they know that this will lead the central bank toraise the short-term interest rate. Even if the Fed doesn’t respond imme-diately, long yields may rise in anticipation of future interest-rate changes.Ditto a high output number: Short- and long-term interest rates rise. Thetiming may differ somewhat from the rule, but its overall impact is generallysimilar.

There are several issues you run across in practice. One is that the Fed(or other central banks ) may deviate from the rule, perhaps on principle,perhaps because of special circumstances. Despite its widespread use, nocentral bank is on record saying that it follows such a rule. Another isthe difficulty in determining y∗. If output goes up, do we decide that theeconomy is overheating and raise the interest rate? Or do we decide thatproductivity has gone up, increasing the growth of the economy and y∗?That’s exactly the issue that the Fed faced in the late 1990s. Some felt thatthe rule dictated higher interest rates, but Greenspan argued that y∗ hadgone up because productivity growth had accelerated. This goes back toour distinction between supply shocks and demand shocks. In the AS/ADframework, demand shocks should generally be resisted, but supply shocksshould be accommodated/acquiesced to. Yet another issue is that the nor-mal real interest rate r∗ may change over time (for example, it might behigh when productivity growth is high, reflecting the marginal productivityof capital).

Despite these open issues, the Taylor rule has been a useful guide to policyand a helpful indicator of how bond markets respond to announcements ofmacroeconomic activity.


15.6 Deflation

Some people are concerned with the possibility of deflation: a decline inprices or negative inflation. There are two good reasons for this. One is acouple of well-documented episodes in which deflation was associated withpoor economic performance: the US in the Great Depression and Japanin the 1990s. The other reason is that deflation raises the real value ofdebt, which makes it more difficult for borrowers to repay them. Modesttemporary deflation is unlikely to have much effect, but large sustainedunexpected deflation, such as the US experienced in the early 1930s, likelyhas an adverse effect on the economy.

Whether that’s the case or not, the issue comes up regularly in policy discus-sions. Examples include Japan during the 1990s, the US during the financialcrisis, and Europe today.

15.7 Quantitative easing, credit easing, and signaling

If the short-term interest rate falls to zero, or close to it, is the centralbank powerless? This issue came up in Japan in the 1990s and much of thedeveloped world after 2008. The answer is no, but let’s review the logic —and the collection of acronyms that go along it.

The so-called zero lower bound (ZLB) is a practical limit on how low nominalinterest rates can go. Why can’t they go lower? Because currency guaranteesa nominal interest rate of zero, so there’s no reason to accept anythinglower. Transaction costs and regulations that give preference to short-termgovernment securities have let interest rates go a little below zero, but, as apractical matter, that’s the limit.

If you follow (say) a Taylor rule and it indicates a negative interest rate,what do you do? Your first guess might be that you’re stuck: zero is it. Butremember: You can always increase the money supply, even if it doesn’t leadto a fall in the nominal interest rate. This change in the quantity of moneyis generally referred to as quantitative easing (QE). For those of us whogrew up thinking about monetary policy in terms of the supply of money,this has a back-to-the-future ring to it: Isn’t that how we used to talk? Thekey is the new terminology, which makes an old idea sound modern. Thatmarketing lesson apparently works as well in economics as with consumerproducts.

In contrast to QE, which increases the size of the central bank’s balancesheet, credit easing (CE) shifts the composition of the balance sheet from


default-free assets toward assets with credit (or other kinds of) risk. Aclassic example of CE is for the central bank to sell Treasury debt and buymortgage-backed securities of the same maturity. Another example is toexchange short-term assets for long-term assets (as in the Fed’s so-calledOperation Twist). Only the mix of assets has changed. CE is thought tolower the cost and increase the supply of credit, particularly when privatemarkets are illiquid.

A different approach to policy at the ZLB is to commit future monetarypolicy to keeping interest rates low. If policymakers believe that inflationwill stay below their target, they can promise to keep their interest-ratetarget low for an extended period. The Fed has used forward guidenceextensively since 2008, and occasionally before that.

Executive summary

1. Most central banks use interest rates as their primary policy tool.

2. Theory and experience suggest that monetary policy should emphasizeprice stability and predictability.

3. The Taylor rule is an approximate description of how central banks setinterest rates: They raise them in response to increases in inflation andoutput.

4. When interest rates hit zero, central banks can still implement policythrough quantitative easing, credit easing, or commitments to future pol-icy actions.

Review questions

1. Real and nominal interest rates. Consider the following informationabout inflation and US interest rates. If we ignore the difference be-tween actual and expected inflation, what was the real interest rate ineach year presented in the table? When was it highest?

Inflation Rate One-Year yield

1980 8.75 12.051990 3.80 7.882000 2.15 6.112010 1.33 0.32


Answer. The real interest rates for the four dates were 3.30, 4.08, 3.96,and –1.01. The highest was 1990, but 2000 is close. By far the lowest is2010.

2. Money supply mechanics. How does a central bank increase the moneysupply? What is the likely effect on the short-term interest rate?

Answer. It purchases government bonds from private agents, giving themmoney in return. An increase in the money supply reduces the short-terminterest rate. The argument is that this increases liquidity in markets,reducing the rate. It depends on an overall environment of price stability.

3. Taylor rule in action. If the inflation rate rises, how would a central bankfollowing a Taylor rule respond? Why?

Answer. It would raise the interest rate. Note that the interest rate risesby more than one-for-one with inflation.

4. The Cleveland Fed has a beautiful chart that describes the asset sideof the Fed’s balance sheet since January 2007. Search: “Cleveland fedcredit easing.” Which features of the chart represent quantitative easing(QE)? Which represent credit easing (CE)?

Answer. The large increase in the size of the Fed’s asset positions in2008 represents QE. CE is less striking in its timing, but the increase inmortgage-backed agency debt (brown) in 2009 is a good example.


For more on the art and science of monetary policy:

• Ben Bernanke’s speeches are typically clear and thoughtful. See especially:

– “Constrained discretion,” February 2003.

– “The Logic of monetary policy,” December 2004.

– “Implementing Monetary Policy,” March 2005.

• The Cleveland Fed’s Taylor rule guide.

http://www.clevelandfed.org/research/data/credit_easing/index.cfm

http://www.federalreserve.gov/boarddocs/speeches/2003/20030203/default.htm

http://www.federalreserve.gov/boarddocs/Speeches/2004/20041202/default.htm

http://www.federalreserve.gov/BoardDocs/Speeches/2005/20050330/default.htm

https://www.clevelandfed.org/research/commentary/2003/0703.pdf



Variable Source

Federal funds rate FEDFUNDS2yr Treasury yield GS210yr Treasury yield GS10Moody’s Baa corporate yield BAABofA Merrill public sector BAMLEMPBPUBSICRPIEY

emerging market yieldCBO real potential GDP GDPPOTReal GDP GDPC1consumer price index CPIAUCSL

To retrieve the data online, add the identifier from the source column tohttp://research.stlouisfed.org/fred2/series/. For example, to retrieve theFederal funds rate, point your browser to http://research.stlouisfed.org/

fred2/series/FEDFUNDS



Symbol Definition

πe Expected Inflationi Nominal interest rater Real interest rate (= i− πe)qm Price of m-year bondim Nominal interest rate or yield on m-year bondπem Expected Inflation over m yearsM Money stockV (i) Velocity of money as a function of interest rate iP Price levelY Real output or GDPY ∗ Equilibrium or potential real outputr∗ Equilibrium real interest rateπ∗ Target inflation ratey Natural logarithm of Y (= ln[Y ])y∗ Natural logarithm of Y ∗

a1, a2 Coefficients or weights in Taylor rule


http://research.stlouisfed.org/fred2/series/FEDFUNDS

http://research.stlouisfed.org/fred2/series/FEDFUNDS


Part IVCrises and Other Topics

201

Crisis Overview

This outline covers key concepts from the third part of the course: macroe-conomic crises and other topics. It is not exhaustive, but is meant to helpyou (i) anticipate what is coming and (ii) organize your thoughts later on.

Taxes and Government Debt and Deficits

Tools: Welfare triangles; government budget constraint; debt dynamics.

Key Words: Tax wedge; deadweight loss; primary deficit/surplus.

Big Ideas:

• Tax systems should be (i) administratively simple and transparent and(ii) have a broad tax base.

• Government spending must be paid for, either now through taxes, or inthe future by running primary surpluses.

• Changes in the ratio of debt to GDP have three sources: interest, growth,and primary deficits.

International Capital Flows

Tools: Balance of international payments; dynamics of net foreign assets.

Key Words: Current account; net exports; capital account; capital flows;net foreign assets.

203


Big Ideas:

• A current account deficit means that a country is borrowing from the restof the world; a current account surplus means it is lending to the rest ofthe world. We refer to the former as a capital inflow and the latter as acapital outflow.

• A capital inflow (borrowing) can lead to problems if it does not supportproductive activities.

Exchange-Rate Fluctuations and Exchange-Rate Regimes

Tools: Arbitrage arguments; central bank balance sheet.

Key Words: Real and nominal exchange rates; purchasing power parity;covered/uncovered interest parity; spot and forward exchange rates; thecarry trade; convertibility; capital mobility; capital controls ; fixed (pegged)vs. flexible (floating) exchange rate regimes; foreign exchange reserves; ster-ilization; speculative attack.

Big Ideas:

• Short-run movements in real exchange rates are largely unpredictable.

• Countries adopt different exchange rate regimes: fixed, floating, and inbetween. The trilemma limits our policy options: we can choose only twoof (i) fixed exchange rate, (ii) free flow of capital, and (iii) discretionarymonetary policy.

• Fixed exchange rate regimes must be defended through open market op-erations and are vulnerable to speculative attack.

Macroeconomic Crises

Tools: Crisis triggers and indicators.

Key Words: Sovereign default; bank runs and panics; refinancing (rollover)risk; leverage; conditionality; solvency and liquidity.

Big Ideas:

• Common triggers of macroeconomic crises are sovereign debt problems,financial fragility, and fixed exchange rates.

• Measures related to these triggers can help identify countries in trouble:debt and deficits, financial weakness, exchange rate regime, and so on.

• The goals of crisis prevention and crisis management are often at odds.

16Taxes

Tools: Welfare analysis; triangles.

Key Words: Tax wedge; welfare loss; social cost; tax rate; tax base.

Big Ideas:

• Tax systems should be (i) administratively simple and transparent and(ii) have a broad tax base.

• A broad tax base minimizes the social cost of taxes.

Governments are a fact of life. They are the central player in building andenforcing the institutional arrangements that make life as we know it possi-ble. They are also, in some cases, an obstacle to performance. The differencebetween good and bad economic performance is often the difference betweengood and bad government.

Our focus will be on the narrower issue of government revenues and expenses.Governments around the world differ in how much they spend (generallymeasured as ratios to GDP), what they spend it on, and how they financetheir spending (taxes and borrowing).

This chapter is devoted to taxes. Taxes are mind-numbingly complicated,but these three principles describe good tax systems:

• Tax revenue pays for spending. A government must collect enoughtax revenue to pay for its expenses, whatever they might be.

205


• Broad tax base. Most tax systems are riddled with exemptions.The problem with exemptions is that they leave non-exempt activities tofinance government spending. With a narrower tax base, the rate mustbe higher on what’s left.

• Administratively simple and transparent. The tax systems in somecountries are so complex that people spend days or weeks of their time,or hire professionals, to figure out what they owe. Worse, some countriesassess taxes in ways that seem arbitrary, leading to unpredictable taxexpenses and endless disputes. The best systems are simple (it’s not hardto figure out what you owe) and transparent (you know ahead of time thetax consequences of your actions).

We’ll focus on the second principle, leaving the first for the next chapterand the third to speak for itself. But if you’re interested in an example of acomplex tax system at work, search “vodaphone taxes India.”

16.1 Social cost of taxes

Taxes are a necessary evil; governments, like people and businesses, mustfinance their spending one way or another. Governments generally do itwith taxes. However, the way in which governments collect tax revenuecan affect economic performance and welfare. Our issue is not that taxestake purchasing power away from individuals. They do, but if governmentspending must be financed, that’s really a question of whether the purchasingpower they take is put to good use. We’ll leave you to decide that foryourself. Our issue is that taxes inevitably discourage some activities relativeto others. Taxes on labor income may discourage work, taxes on capital (orinvestment) income may discourage saving and investment, and taxes oncigarettes may discourage smoking. We’ll leave cigarettes for another time,but the general incentive effects of taxes are worth a closer look.

More formally, taxes affect (“distort”) economic decisions. They insert a“wedge” (a difference or discrepancy) between private and social costs ofvarious activities. As a result, they generally lead to decisions that aresocially inefficient: We could reallocate the same resources and raise every-one’s welfare. The conditions for this invisible-hand result should be familiarfrom your microeconomics class: clear property rights, competitive buyersand sellers (no monopolies), complete information, and absence of external-ities (no direct impact of one person’s actions on another’s welfare). Underthese conditions, we might want to set tax rates to generate the least dis-ruption to resource allocation: to minimize the adverse incentives built intotaxes.

16. Taxes 207

We can get a sense for how taxes affect decisions in a traditional supply-and-demand setting like that in Figure 16.1. The demand curve (labeledD) represents purchasers of the product; for any given quantity Q, it tellsus how much buyers are willing to pay — hence the value to them (at themargin) of that number of units. The supply curve (labeled S) representssellers. With competitive sellers, it tells us how much it costs to produce agiven quantity (at the margin). The market clears at point A, where supplyand demand are equal.

Figure 16.1: The social cost of a tax.

-Q

6P Z

ZZZZZZZZZZZZZZ D"

"""""""""""""" S

""""""""""""""" S′

A

B

C

E

F

G

The social cost of imposing a tax that shifts the supply curve

from S to S′ is the triangle ABC.

Now suppose we charge a tax of a fixed amount per unit. From the per-spective of buyers, the supply curve has shifted up by the amount of thetax to S′. Note that there is now a difference between the social cost (themarginal cost of production in terms of resources used) and the private cost(the price paid by buyers): a wedge, in other words. The market now clearsat B for buyers and C for sellers. This difference leads buyers and sellersto reduce the quantity of resources allocated to this product, leaving themto be used elsewhere in the economy. Buyers, of course, buy fewer units,because the price has gone up. Sellers offer fewer units for sale because theprice to them has fallen.

The social cost of the tax (the reduction in welfare it causes) is the area insidethe triangle ABC. The upper part of the triangle is the loss of consumersurplus (the difference between what buyers pay and what the product isworth to them). The lower part of the triangle is the loss of producer surplus(the difference between what sellers receive and the cost of production).The sum is the social cost of the tax, which economists refer to as the


“deadweight loss” or “excess burden.” You may recall a similar argumentagainst monopolies. Both result in fewer resources devoted to the productthan we would like.

If you’re not familiar with this kind of analysis, here’s a more completeaccounting of the welfare loss. It’s not essential to our story; feel free toskip to the next paragraph. In the figure, the loss of consumer surplus isthe area EBAG, the cost to them of charging a higher price. The loss ofproducer surplus is FCAG. Adding them together gives us an area muchlarger than the triangle ABC. The difference is the rectangle EBCF, whichis the amount of revenue collected by the government. This revenue doesn’tdisappear, so it’s not a welfare loss. That leaves us with the triangle ABCas the welfare loss.

There’s a fine point here about who pays the tax. We could charge sellers orbuyers with the same result. Governments sometimes prefer taxes on firmsto taxes on people, in part because it makes the tax less visible to voters,but the impact on resource allocation should be the same.

16.2 The benefits of a broad tax base

One objective of a good tax system is to minimize the social cost of taxes:to raise tax revenue with as little impact as possible on resource allocation.We sometimes say we’re looking for a resource-neutral tax system — or asclose to neutral as we can get. This is a complicated issue, both in theoryand in practice, but one principle is that we want a broad tax base.

The argument for a broad tax base goes like this. Think about two ways ofraising the same tax revenue: a low tax rate on a broad base and a higherrate on a narrower base. Which is better? We’ll give an answer using oursupply and demand analysis. Suppose we have two similar markets, eachlike the one we described in Figure 16.1. In the broad-base system, we taxthe products in both markets at the same rate. The social cost is, therefore,double what we saw earlier: the triangle ABC for each market.

Now consider a narrow-base system that taxes one market at twice the rate.We’ll use Figure 16.2 to see how this works. There, we have drawn threesupply curves: S refers to supply without the tax; S′ refers to supply witha small tax (the broad-base system); and S′′ refers to supply with a taxrate double that in S′ (the narrow-base system). What is the social costof the narrow base? Since the rate is higher, the welfare triangle is larger;it consists of the area ADE. If you look at this long enough, you’ll realizethat the area of ADE is four times that of ABC, which makes the social costtwice as large as in the broad-base system.

16. Taxes 209

Figure 16.2: The social cost of doubling a tax.

-Q

6P Z

ZZZZZZZZZZZZZZ D"

"""""""""""""" S

""""""""""""""" S′

""""""""""""""" S′′

A

B

C

D

E

We double the tax rate by shifting the supply curve from S to

S′′. Note the social cost: the triangle ADE is four times as big

as ABC.

The point, in general, is that broad-based tax systems are better becausethey allow you to raise a given amount of revenue with a lower rate and(therefore) smaller social cost. You’ll hear lots of arguments for tax exemp-tions, but you rarely hear that they result in higher taxes on other things,which is the primary argument against them.

A corollary of this principle is that with similar goods — by which wemean goods with similar supply and demand curves — we should aim forsimilar tax rates. The reasoning is the same, although it’s harder to showin a diagram. If we have goods whose demand curves have different slopes,similar logic would lead us to tax them differently, but that’s a subtle pointwe’d prefer to leave for another time.

16.3 Applications

Here are some practical applications of the broad-tax-base/tax-similar-goods-the-same principle.

The underground economy. One of the difficulties of an undergroundeconomy is that unofficial businesses typically do not pay taxes, therebyforcing all of the tax burden onto the rest of the economy. That violates ourprinciple (low rate on broad base) and also the corollary (tax similar goods


at similar rates). We’ve shown that this leads to an inefficient allocation ofresources.

William Lewis (The Power of Productivity) argues that in Brazil, it may alsolower productivity. His argument has several steps. Brazil has a relativelylarge government for a country at its stage of development (40 percent ofGDP, which is above the US and significantly above what we see in mostdeveloping countries). Financing government spending requires, therefore,relatively high tax rates, which creates a substantial incentive for tax avoid-ance. Small firms (the story goes) are generally less productive than largefirms (economies of scale), but many survive because they are able to avoidtaxes. Thus the tax system protects inefficient small firms, thereby low-ering overall productivity. In Lewis’s story, this is a direct result of largegovernment.

Value-added taxes (VAT). Before the VAT became popular, countriesoften had piecemeal tax systems in which goods were taxed at every stageof production. This led, in some cases, to very high taxes on intermediateand final products simply because the taxes at each stage added up. Thisviolates our principle, specifically the corollary, because a product made bya single vertically-integrated firm is taxed at a lower rate than the sameproduct made by several firms, one at each stage.

Consider a product that has five stages of production, each performed bya different firm. If each stage is charged a moderate tax of ten percent,what is the total tax paid in the production of the product? Let’s say thattotal value added is five, with one unit of value added at each stage. Thefirst-stage firm produces one unit of value. This costs the second-stage firm1.10 since it must pay the ten percent tax. This firm also adds one unit ofvalue, and sells its output for a price (including taxes) of

(1.10 + 1)× 1.10 = 2.31,

so the implicit tax rate over the two stages is 0.31/2 = 15.5 percent. If youwork through all five stages, you’ll find that the price of the final product,including all the taxes paid, is 6.71 after the last stage, so the effectivetax rate is 34.2 percent [= (6.71 − 5.00)/5.00]. Note the large differencein tax rates across the five stages of production. The final stage only getstaxed once, so it pays a tax rate of 10%, but the first stage gets taxed fivetimes, so it’s taxed at a rate of 61 percent [1.105 = 1.61]! In contrast, avertically-integrated firm pays only ten percent, at each stage and overall.

These differences in tax rates potentially lead to inefficient production, asfirms look for substitutes for highly-taxed inputs, or integrate vertically.This is one of the arguments for a value-added tax system. With a VAT,

16. Taxes 211

firms pay tax on only the value-added of their stage of production, whicheliminates differences in tax rates paid by different stages. A value-addedtax system is equivalent to one in which we tax only the final good; we justarrange to collect the tax in pieces.

Taxes on capital income. A high tax rate on capital income mightbe expected to discourage saving and investment, leading the economy tohave less capital than otherwise. This, in turn, would reduce wages, sincethe marginal product of labor is lower if we have less capital. So, what isan appropriate tax rate on capital income? Some economists argue thattaxes on capital income should be zero. People would eventually pay taxon capital income indirectly when they consume the proceeds, but theyshould not be taxed before then. The logic is similar to the argument for avalue-added tax, since taxes on capital income are effectively taxes on futureconsumption and accumulate in a similar way.

Let’s think about how households allocate their income over time. Supposethat we have two dates (labeled “0” and “1”). If a household earns laborincome (Y0, Y1) at the two dates and receives a (real) interest rate r onsaving, then saving is Y0 − C0, and consumption at date 1 must be C1 =(1 + r)(Y0 − C0) + Y1. We can put the two together in the present-valuerelation:

C0 + C1/(1 + r) = Y0 + Y1/(1 + r).

This tells us, in essence, that the price of date-1 consumption is 1/(1 + r).If we had more periods, we’d have a similar relation, with prices 1/(1 + r),1/(1 + r)2, 1/(1 + r)3, etc., for consumption at dates 1, 2, 3, etc.

Now think about taxes. If we tax interest income, this changes the priceof future consumption. For a given real interest rate r, a higher tax rateincreases the price of future consumption, which you might expect to en-courage current consumption. If the tax rate on capital income is τ , thenthe after-tax interest rate is (1 − τ)r and the price of consumption n peri-ods in the future is 1/[1 + (1 − τ)r]n. This may not seem like a big deal,but with the mythical power of compound interest, it can increase the priceof future consumption substantially. Consider a numerical example withr = 0.04 (four percent a year) and a tax rate of τ = 0.25 (25 percent).With no tax, the price of consumption one period in the future is 0.9615[= 1/(1 + r)]. With the tax, this increases to 0.9709 [= 1/[1 + (1 − τ)r]],a modest difference. But if the number of periods is large, the differencecan also be large. Suppose n = 25; think of a 30-year-old consultant savingfor retirement. Then, the tax raises the price of future consumption by 27percent, from 0.3751 to and 0.4776. You can imagine that this could leadpeople to consume more now and less later since future consumption has


become relatively more expensive. It might also lead them to work less ifworking now is intended to finance future consumption.

If people consume more now and less later, then they are saving less. Andif they are saving less, the economy will have less capital. The cost has thesame source as in our earlier analysis: The private benefits of saving are lessthan the social benefits, so we do too little of it. That’s why some economistsfavor a consumption tax: a tax on only that part of income that is consumed.In practice, many countries offer something of this sort through tax-shelteredretirement and saving programs, which avoid the period-by-period tax oninvestment income of our example.

If a government promises not to tax capital too heavily in the future, willinvestors believe it? This version of the time-consistency problem can besevere. If investors doubt the commitment, they will refrain from investmenteven if current tax rates are low. The issue arises whenever governments areseen as willing to exhaust their borrowing capacity. As we have seen inother examples, overcoming the challenge of time consistency depends onthe nature and quality of a society’s institutions. In the late 17th century,for example, the empowerment of the British parliament helped persuade arising commercial class that the King would not arbitrarily seize their wealth.The flow of savings and investment helped Britain grow earlier and fasterthan other modern economies. In many highly indebted countries today,concerns about future tax burdens can reduce saving and investment now, orencourage other means of tax avoidance, possibly making the government’scurrent budget situation worse.

Changing tax rates. Economist Edward Prescott writes (Wall StreetJournal , December 20, 2005):

Let’s drop the word “cuts” [when we talk about taxes]. Theproblem with advocating a cut in something is that you are nec-essarily going to stir up political trouble from someone who willwant to increase it again. So, even if you are fortunate enoughto get your cut enacted, it is likely a matter of time before thepolitical pendulum swings back and someone else gets their in-crease.

The argument against large changes in tax rates over time follows fromthe corollary: “Tax similar markets at similar rates.” In this case, thetwo markets are “today” and “tomorrow.” We could add the cost of theuncertainty created by the process of changing tax rates.

16. Taxes 213

Deficits. The same argument gives us some insight into deficits. We shouldfinance whatever the government spends with relatively stable tax rates.Why? Because low taxes now and high taxes later, or the reverse, violatesour principle. Suppose, then, that the government is running a deficit.Should it raise taxes? It should aim at a stable level of tax rates thatfinances government spending. Typically, you would expect this to lead todeficits in recessions, when the tax base is small, and surpluses in booms. Inpractice, this is more complicated because we don’t know either the level ofspending (what’s the present value of future commitments to Social Securityand Medicare?) or the base on which tax rates will be applied (will theeconomy grow three or four percent a year over the next decade). Theprinciple remains: finance government spending with stable tax rates.

Executive summary

1. All taxes have incentive effects. In the absence of externalities and mo-nopolies, the tax systems that lead to the most efficient allocations ofresources (a) apply low tax rates to a broad base and (b) tax similarproducts at similar rates.

2. The cost of exemptions is that non-exempt products must pay higherrates as a result.

Review questions

1. Welfare triangle review. In Figure 16.1, identify the following:

(a) The loss of consumer surplus. Why does the tax leave consumerswith less surplus?

(b) The loss of producer surplus. Why does the tax leave producers withless surplus?

(c) Government revenue.

(d) The total welfare loss.

Answer.

(a) The area EBAG. consumer surplus before the tax is the area betweenthe demand curve and the line GA indicating the market price. Someconsumers are willing to pay more; the difference is their surplus.When the price paid by consumers rises as a result of the tax, someof this surplus goes away.

(b) The area FCAG. Producer surplus before the tax is the area betweenthe supply curve (the cost of production) and the line GA indicatingthe market price. When the price received by producers falls as aresult of the tax, some of this surplus goes away.


(c) The area EBCF. this is the tax (EF) times the equilibrium quantity(FC).

(d) The area ABC. This is consumer surplus plus producer surplus minusgovernment revenue.

See also the discussion at the end of Section 16.1.

2. Tax systems. Comment on the welfare impact of these aspects of the UStax system:

(a) Sales tax exemption for food and clothing.

(b) Sales tax exemption for goods purchased over the internet.

(c) Sales tax exemption for medical care.

(d) Income tax exemption for health insurance.

(e) Sales tax exemption for education supplied by nonprofit institutions.

(f) Elimination of the capital gains tax.

Answer.

(a) Probably bad because it means tax rates on other things must behigher, which generates larger welfare losses. Remember: broadbase, low rates. One common justification is that it favors poorpeople, since food and clothing are necessities, but it’s probably notan effective way to do this. The best way is simply to give themmoney.

(b) Also bad, and for the same reason. It leads to such things as salestax on internet purchases from Barnes & Noble (since they havelocal outlets) but not on Amazon (since they do not).

(c) Ditto.

(d) Ditto.

(e) Remember the principle: tax similar products the same way. There’sno economic logic for taxing a product differently just because itsproducer it has a different legal structure. Remember: the NYSEwas a nonprofit until recently.

(f) To the extent that it’s a tax on capital or investment income, thiscould be a good thing. Further, capital gains reflect inflation as wellas investment income, which can result in potentially very high taxrates on real returns. The solution here, though, is to index thetax system (or keep inflation low enough that it doesn’t have mucheffect). An important caveat is that there are no adverse incentiveeffects involved in taxing capital gains that have already occurred;the incentive argument works only going forward.

16. Taxes 215

3. Taxes without spending? Suppose a hypothetical government has noexpenditures to finance. What tax rates should it set?

Answer. Zero! Why? Nonzero taxes (even negative taxes or subsidies)generate adverse incentives; the prices people pay for products do notreflect their social cost of production. Possible exception: externalities,although even here there may be better choices than taxes.

4. Small government. Since government spending must be financed withtaxes, and taxes distort the allocation of resources, should we have asmall government?

Answer. This is a complex issue, but here’s one take on it. First, you needa government. There are clearly important and necessary roles for gov-ernment: providing national and personal security, defining and enforcingproperty rights, supporting competitive markets, and so on. Without aneffective government, you simply can’t have a productive economic sys-tem. Second, there’s tremendous variety across countries in the kinds ofservices provided by government. In many countries, governments supplyeducational services, social insurance, and pensions, although the degreeof government involvement varies. The evidence is mixed. Among coun-tries with high GDP per person, those with large governments are notnotably less productive than those with small governments. Sweden, forexample, is a productive and prosperous country despite very high gov-ernment spending. Among developing countries, the evidence is stronger:Those with smaller ratios of spending to GDP have grown faster, on av-erage, over the last forty years. This may reflect the direct effects ofgovernment or other factors — it’s hard to say.

5. Progressive taxes. Questions often come up about the progressivity oftax systems. They aren’t really review questions, but this seems as gooda place to put them as any.

(a) How does a progressive tax square with taxing similar things atsimilar rates?

(b) Since rich people own most of the assets, shouldn’t we tax investmentincome as a way to redistribute income?

(c) If we rely heavily on VAT, as many countries do, how do we makethe overall tax system progressive?

Answer.

(a) It doesn’t. For reasons we’ve seen, progressive taxes distort resourceallocation more than a flat tax that collects the same amount ofrevenue. But they also redistribute income from rich to poor. If youwant the latter, you’re stuck with some of the former.

(b) Maybe. It still has adverse incentive effects, but it’s true that wealthis much more unequally distributed than income.


(c) A VAT is, by design, a flat tax: products and people are treated thesame way. In practice there’s some variation in rates by products,but it’s harder to treat buyers differently. Most countries introduceprogressivity through the income tax and means-tested benefits.


The analysis of welfare triangles is standard economics. See, for example,these links from Wikipedia:

http://en.wikipedia.org/wiki/Economic_surplus

http://en.wikipedia.org/wiki/Deadweight_loss

There’s also a Khan Academy video (“Taxation and dead weight loss”).

Real-world tax systems can be incredibly complicated. Some good overviewsare:

• The OECD’s program on taxation has an extensive set of data and analysisfor developed countries:

http://www.oecd.org/tax/.

• The World Bank’s Doing Business website includes information about taxrates and associated administrative costs for mid-sized firms. Be careful,however, of the definitions. Total tax, for example, is reported as a per-centage of profit, even though some of the taxes apply to labor.

• The Economist Intelligence Unit’s Country Commerce and Country Fi-nance reports contain information about both business and individualtaxes. Here’s what they say about corporate taxes in the US: “Tax ju-risdiction in the United States is divided among the federal government,the 50 states plus the District of Columbia, and local counties and mu-nicipalities. ... There are no uniform rules on the definition of taxableincome or on the apportionment of income among the various tax juris-dictions. Hence, the advice of a tax lawyer is practically indispensable toany newcomer to multistate business.”

• Myron Scholes, Mark A. Wolfson, Merle Erickson, Edward Maydew, andTerrence Shevlin’s Taxes and Business Strategy (4e) is a wonderful, prac-tical book on tax issues. (Earlier editions are cheaper, and probably asgood for our purposes.)

http://en.wikipedia.org/wiki/Economic_surplus

http://en.wikipedia.org/wiki/Deadweight_loss

http://www.oecd.org/tax/

16. Taxes 217



Symbol Definition

P PriceQ QuantityS SupplyD DemandY Labor incomeC Consumptionr Real interest rateτ Tax rate (proportional)


17Government Debt and Deficits

Tools: Government budget constraint; debt dynamics.

Key Words: Government budget; government debt and deficits; primarydeficit/surplus; the debt-to-GDP ratio; hidden liabilities.

Big Ideas:

• Government spending must be paid for, either now through taxes, or inthe future.

• Current debt must be balanced by future primary surpluses.

• Changes in the ratio of debt to GDP have three sources: interest, growth,and primary deficits.

The first principle of government finance is that governments must financespending with taxes. Issuing debt postpones this obligation but does noteliminate it. If a government doesn’t collect enough tax revenue now, itmust collect it later — or face default. Since investors like to be repaid,they pay close attention to government debt and deficits. If they’re toolarge, investors may demand higher yields or even stop buying governmentsecurities altogether. The consequences of this sequence of events are neverpretty.

Debt finance poses a time-consistency problem because (i) governments havean incentive to issue debt and tax future generations who do not vote today;and (ii) future governments may decide to inflate away or repudiate pastdebt. Countries with good governance solve this problem either throughsound budget policy or institutional design. Countries with poor governance,not so much.

219


17.1 Government revenues, expenses, and debt

We start with a quick overview of government spending and revenue deci-sions — what is conventionally called fiscal policy .

Countries differ in the size of government relative to the economy, in thesources of tax revenues, and in their expenditures. Governments everywherepurchase goods and services (schools, police, courts, roads, military), trans-fer money to individuals (social insurance, health care), and collect revenue(largely through taxes). The distinction between purchases and transfers isimportant. Only purchases show up in the expenditure identity. Transfersare, nevertheless, a large part of total expenses in many economies, partic-ularly developed economies. Governments also pay interest on outstandinggovernment debt, an expense we track separately.

We’ll look at data for each of these in class. As a rule, government spendingand revenue are a larger fraction of GDP in rich countries than in poorones. Rich countries also spend more on transfers. There is, however, a lotof variation at all levels of development.

We put these elements together in a relation we’ll call the government budgetconstraint. On the expense side, we label government purchases of goodsand services G, transfers V , and interest payments iB (the product of thegovernment debt B and whatever interest rate i the government pays on it).On the revenue side, we label tax revenue T . (Note: T is tax revenue, not thetax rate.) By convention, all of these things are nominal: they’re measuredin local currency units. The government budget constraint is, then,

Gt + Vt + itBt−1 − Tt = Bt −Bt−1. (17.1)

Here, Bt−1 is the amount of debt outstanding at the end of period t − 1.The left-hand side of (17.1) is the government deficit, the right the changein the quantity of debt. The equation says, in essence, that any surplus ordeficit is matched by a change in the quantity of debt. A government deficitis financed by issuing more debt.

The elements of equation (17.1) are often used to generate summary mea-sures of fiscal policy. The most common are ratios of the government deficitand government debt to GDP. We’ll look at both, as well as the connectionbetween them.

17.2 Debt and (primary) deficits

Governments need to finance their spending with taxes. It’s not quite true— governments have other sources of revenue — but it’s close enough to be

17. Government Debt and Deficits 221

worth remembering. Issuing debt allows a government to postpone taxes,just as a credit card allows an individual to postpone paying for purchases,but does not eliminate the obligation. Delay, in fact, comes with a cost: Weneed to pay the original obligation, plus interest. In the rest of this section,we make the same point more formally.

We’re going to take our budget constraint, equation (17.1), and use it torelate debt to past and future deficits. To make things a little simpler,define the primary deficit D as the deficit net of interest payments (sort ofan “EBITDA” number):

Dt = Gt + Vt − Tt.

(This is sometimes reported with the opposite sign and called the primarybudget balance or surplus.) With this simplification, (17.1) can be expressedas

Bt = (1 + i)Bt−1 +Dt (17.2)

or

Bt−1 = Bt/(1 + i)−Dt/(1 + i). (17.3)

They’re the same equation, but the first one looks backward from t to t− 1,and the second looks forward from t− 1 to t. We’ll put both to work. The iin these equations is the nominal interest rate that the government pays onits debt. We’ll assume it is constant for now — it makes the math simpler— but allow it to change in the next section.

Equation (17.2) tells us where the debt came from. If we substitute overand over again, back to some period t− n, we have

Bt = Dt + (1 + i)Bt−1

= Dt + (1 + i)[(1 + i)Bt−2 +Dt−1]

= Dt + (1 + i)Dt−1 + (1 + i)2Dt−2 + · · ·+ (1 + i)nBt−n.

In words: The current debt is the debt we started with n periods ago plus thecurrent value of past deficits plus accumulated interest. It’s like your creditcard bill: Your current balance consists of past shortfalls plus accumulatedinterest.

Equation (17.3) tells us what we need to do in the future to service thecurrent debt. If we substitute repeatedly, we find

Bt−1 = Bt+1/(1 + i)2 − [Dt/(1 + i) +Dt+1/(1 + i)2]

= Bt+2/(1 + i)3 − [Dt/(1 + i) +Dt+1/(1 + i)2 +Dt+2/(1 + i)3]

= Bt+n−1/(1 + i)n − [Dt/(1 + i) + · · ·+Dt+n−1/(1 + i)n].


If we assume that debt can’t grow faster than the interest rate forever, then,as we continue to substitute, the first term goes to zero. [The technicalcondition is Bt+n/(1 + i)n approaches zero as n approaches infinity. Itamounts to not allowing the government to run a Ponzi scheme, paying offold debt by issuing new debt, forever.] The relation then becomes

Bt−1 = −[Dt/(1 + i) +Dt+1/(1 + i)2 +Dt+2/(1 + i)3] + · · · ]= −Present Discounted Value of Primary Deficits

= Present Discounted Value of Primary Surpluses. (17.4)

In words: The current government debt must be matched by the presentdiscounted value of future primary surpluses. As we said at the start, allspending must be financed by tax revenue — eventually. It’s not enoughto shrink the deficit. Eventually we have to run surpluses, measured net ofinterest payments.

Analysis of this sort often uses the term sustainable. We say the debt issustainable if current debt is balanced by plans for future surpluses, as inequation (17.4). If not, we say the government’s budget is unsustainable.In this case, we can paraphrase the economist Herbert Stein: “Somethingmust change, so it will.”

17.3 Debt dynamics

Investors watch government debt and deficits for signs that a governmentmay not honor its debts. Even a hint of this can change the rate at whichthe government borrows or even its ability to access capital markets. Inpractice, it’s common to look at them as ratios to GDP. In such ratios, wemeasure both numerator and denominator in local currency units, so wehave (for example) the ratio of the nominal debt to nominal GDP.

So how does the debt-to-GDP ratio change from one period to the next?There’s a useful decomposition of changes into components due to the realinterest rate, GDP growth, and the primary deficit. It’s a little complicated,so we’ll work our way up to it.

Recall that debt evolves according to

Bt = Dt + itBt−1 +Bt−1, (17.5)

where Dt is the primary deficit and Dt + itBt−1 is the total deficit. Youshould recognize this as equation (17.2) in slightly different form. Here’show it looks with real numbers.

Example (US, 2013). Consider US government debt and deficits in 2013,expressed in trillions of US dollars:


Government debt, year end 2012 Bt−1 13.015Total deficit, 2013 Dt + itBt−1 1.233Primary deficit, 2013 Dt 0.693

The numbers are estimates from the April 2014 edition of the IMF’s WorldEconomic Outlook database. Given these numbers, use what we know aboutdebt dynamics to compute debt Bt at the end of 2013. How much interestwas paid on debt? What is the interest rate it paid on the debt?

Answer. Year-end debt follows from equation (17.5): Bt = 1.233 + 13.015 =14.248. Interest payments are the difference between the two deficit num-bers: itBt−1 = Dt + itBt−1 − Dt = 1.233 − 0.693 = 0.540. The im-plied interest rate on the debt is the ratio of interest payments to debt:itBt−1/Bt−1 = 0.540/13.015 = 0.0415 = 4.15%.

Now back to the dynamics of the debt-to-GDP ratio. The bottom line isthe equation

BtYt

≈ Bt−1Yt−1

+ (it − πt)Bt−1Yt−1

− gtBt−1Yt−1

+Dt

Yt. (17.6)

Circle this, it’s important. It gives us three sources of change in the ratio ofdebt to GDP. The first is the real interest on the debt, which accumulates aslong as the debt and real interest rate are positive. The second is the growthof the economy, which reduces the ratio by increasing the denominator. Thethird is the primary deficit. Each makes a contribution to changes in thedebt-to-GDP ratio.

It’s not required, but if you’re interested in where this comes from, here arethe details. We divide equation (17.5) by nominal GDP Yt to get

BtYt

=Dt

Yt+ (1 + it)

Bt−1Yt

.

In the last term, note that the denominator is Yt, not Yt−1. If the growthrate of real GDP is gt and the inflation rate is πt, then the growth rate ofnominal GDP is approximately gt + πt. Therefore

Yt ≈ (1 + gt + πt)Yt−1.

The ratio of debt to GDP then follows

BtYt

≈(

1 + it1 + gt + πt

)Bt−1Yt−1

+Dt

Yt

≈ [1 + it − (gt + πt)]Bt−1Yt−1

+Dt

Yt

≈ Bt−1Yt−1


− gtBt−1Yt−1

+Dt

Yt.

http://www.imf.org/external/ns/cs.aspx?id=28

http://www.imf.org/external/ns/cs.aspx?id=28


The second equation is based on the approximation

1 + it1 + gt + πt

≈ 1 + it − gt − πt,

good for small values of it, gt, and πt. A simpler version is 1/(1+x) ≈ 1−xfor small x. All you need to know is that the right side is simpler than theleft. After rearranging terms, we’re left with (17.6), as promised.

This is a mechanical analysis, but a useful one. By looking at the compo-nents of equation (17.6), we can get a sense of the origins of past changes inthe debt-to-GDP ratio and the potential sources of future changes.

Example (US, 2013, continued). The numbers we saw earlier look thisway expressed as ratios to GDP:

Government debt, year end 2012 Bt−1/Yt−1 0.8012Primary deficit, 2013 Dt/Yt 0.0413Interest rate it 0.0415Real GDP growth rate gt 0.0188Inflation rate πt 0.0151

What is the ratio of debt to GDP at the end of 2013?

Answer. We apply the formula, equation (17.6):

Bt/Yt = 0.8012 + (0.0415− 0.0151)0.8012− (0.0188)0.8012 + 0.0413

= 0.8012 + 0.0212− 0.0151 + 0.0413 = 0.8486.

In words: the ratio of debt to GDP rose from 80.1 percent to 84.9 percent, anincrease of 4.8 percent of GDP. The primary deficit contributes 4.1 percentof the change and growth drives it the other way by 1.5 percent.

Comment. We have two sets of numbers here that are often expressed aspercentages, meaning we multiply them by one hundred. One is the “growthrates”: g, i, and π. For them, it’s essential we use numbers, not percentages.You might verify that we did this in the calculation above. You’d see thesame when you calculate a present value in finance. The second set ofnumbers is the ratios to GDP: B/Y and D/Y . These can be used either asnumbers, as in the example above, or percentages, as long as we treat themboth the same way. If we use percentages in our example, equation (17.6)becomes

Bt/Yt = 80.12 + (0.0415− 0.0151)80.12− (0.0188)80.12 + 4.13

= 84.86.


Evidently the equation still works when we multiply it by one hundred.

Example (Peru, 2003-2007). Between 2003 and 2007, Peru’s debt fellfrom 47 percent of GDP to 25 percent. Using the numbers in the tablebelow, what happened? What was the primary source of this decline?

Debt Interest Growth DeficitBt/Yt (it − πt)Bt−1/Yt−1 −gtBt−1/Yt−1 Dt/Yt

2003 47.12004 44.3 0.2 −2.4 −0.62005 37.7 1.1 −3.0 −4.62006 33.1 1.0 −2.9 −2.72007 30.9 1.1 −2.9 −0.42008 25.0 −0.3 −3.0 −2.5

Sum 3.1 −14.3 −10.9

Answer. Between 2003 and 2008, the ratio of debt to GDP fell from 47.1%to 25.0%, a change of −22.1%. What factors were most important? Youcan see from the final row that growth (−14.3%) and the primary deficit(−10.9%) both played large roles. Interest on the debt pushes us the otherway: it raises the ratio of debt to GDP (+3.1%).

17.4 What’s missing?

Our summary of debt dynamics, captured in equation (17.6), buries someissues beneath the mathematics.

One issue is the link between the interest rate and the fiscal situation (thedebt and deficit). If investors start to worry about a government’s willing-ness to honor its debt, they may demand higher interest rates, which, inturn, raises future debt — and so on. Such credit spreads can rise sharply ifthe government has not shown sufficient fiscal discipline. (Here, “sufficient”means whatever is needed to reassure investors.) It can also rise becauseglobal financial markets place a higher premium on risk, as they did duringthe 2008-09 financial crisis. Over this period, spreads on emerging marketdebt of all kinds widened, even in countries with fundamentally sound fiscalpositions.

Another issue is the link between growth and deficits. If growth rises, asin Peru (example, above), that reduces the debt-to-GDP ratio through the


impact on g in equation (17.6). But it also generates higher tax revenuesand, hence, a lower primary deficit, even if tax rates do not change. This,in turn, reduces future debt further. That’s one reason that Peru’s fiscalsituation improved: The economy boomed. Growth, then, is the cure formany problems.

A third issue is hidden government liabilities. The idea behind our analysisis that the primary deficit determines how the debt evolves. In fact, currentdecisions often involve commitments for future expenditures that don’t showup in the current government budget but are nevertheless important. Inprinciple these hidden liabilities should show up in the budget when they’reincurred, but in practice they don’t. Here are some common examples:

• Social security and pensions. Many countries have implicit commitmentsto pay money to retired people in the future that are not accounted forproperly. In the US, for example, the official accounts are based on thecurrent cash flow of social security receipts and payments. In principle,there should be an entry for unfunded pension liabilities, as there is forfirms. In many countries, aging populations have made these loomingpayments a serious concern. Healthcare payments are similar.

• Financial bailouts. We tend to treat these as one-offs, but, in fact, theyhappen all the time and they’re invariably expensive. A country that bailsout its banks may find its debt rise sharply.

• Regional governments. Relations between central governments and localauthorities differ widely around the world. In the US, the precedent wasset in the 1840s for state and local governments to finance their ownactivities without help from the central government. In other countries,debt problems of regional governments are often passed to the centralgovernment. These implicit liabilities of the central government were aconcern in Argentina and Brazil in the 1990s and in Spain right now.

A serious analysis of fiscal policy should, therefore, start with equation (17.6)but go on to consider all possible sources of change in its components. It’sno different from financial accounting for firms: we need to know what liesbehind the numbers.

17.5 How much debt is too much?

How much debt is too much? At what point should investors be concerned?There is, unfortunately, no clear answer. Or rather there is an answer, whichis that the quality of governance is more important than the debt numbers.Argentina defaulted with debt of about 40 percent of GDP, but the UK had


debt well over 100 percent of GDP after World War II and didn’t generateundue concern. In many cases you’re stuck trying to guess how the localpolitics will play out.

With that warning, here are some rules of thumb:

• Debt. Worry if the government debt is above 50 percent of GDP. This isvery rough, but it’s a start.

• Deficits. Worry if the deficit is above 5 percent of GDP — and is expectedto stay that way. The issue is not so much any particular deficit, but thelong-term posture.

• Institutions. Worry if a country’s political institutions are weak. An oldrule of thumb is that a country’s credit rating is more closely connectedto the quality of its institutions than to the quantity of debt it’s issued.Think to yourself: Argentina is different from the UK, and Germany isdifferent from Greece. The institutions that matter most are those thathelp contain the time-consistency problem: namely, the risk that a futurepolicymaker will repudiate or inflate away the debt. Relevant institutionswould include an independent central bank (to limit inflation), a robust fi-nancial system (that promotes market discipline and limits bailouts), andfiscal arrangements that limit debt accumulation or prevent its repudia-tion (e.g., transparent and comprehensive long-term budgeting, pay-go orbalanced budget rules, and legal requirements for prioritizing debt pay-ments).

• Structure of debt. Worry if the debt is primarily short-term or denomi-nated in foreign currency. Even if the debt is stable, countries may findthemselves in difficulty if they have to refinance a large fraction of theirdebt over a short period of time. (Companies are no different; thinkLehman Brothers, or Drexel before that.) In late 1994, for example, Mex-ico had much of its debt in short-term securities. When investors refusedto buy new issues, it triggered a crisis. This despite relatively modestdebt and deficits.

Foreign debt has similar risks. Many developing countries issue debt de-nominated in hard currency (dollars, say, or euros), but it’s a mixed bless-ing. Issuing debt in hard currency reduces currency risk for investors, butif a country’s currency collapses, it debt can rise sharply, perhaps increas-ing the odds of default. We’ve seen this repeatedly: Mexico in 1994, Koreain 1997, Argentina in 2001, and Iceland in 2008.


Executive summary

1. Countries differ enormously in the magnitude and composition of govern-ment spending, taxes, and debt.

2. Government spending must be paid for, either now through taxes or inthe future by running primary surpluses.

3. The following factors govern changes in the debt-to-GDP ratio: (a) in-terest on the debt; (b) GDP growth; and (c) the primary deficit.

4. Institutions that limit the incentive of future governments to inflate awayor repudiate the debt can help to promote fiscal discipline.

Review questions

1. Deficits down under. Consider this data for Australia:

2010 2011

Real GDP growth (annual percent) 2.6 2.9Inflation (annual percent) 5.2 4.8Interest rate (annual percent) 5.3 5.9Government deficit (primary, percent of GDP) 2.9 0.7Government deficit (total, percent of GDP) 4.1 2.2Government debt (end of period, percent of GDP) 25.3

(a) Why are the primary and total government deficits different?

(b) What is the government debt ratio at the end of 2011?

Answer.

(a) The difference is interest payments on government debt. Apparentlyin 2011 they amounted to 1.5 percent of GDP.

(b) We use the debt dynamics equation:

BtYt

=Bt−1Yt−1


− gtBt−1Yt−1

+Dt

Yt= 25.3 + (0.059− 0.048) ∗ 25.3− 0.029 ∗ 25.3 + 0.7

= 25.6.

We used a shortcut here on the interest rate, taking the number fromthe table (a typical market rate) rather than computing the interestrate paid on government debt.


2. How the US financed World War II. The short answer is that they issueddebt, but how did they pay off the debt? Between 1945 and 1974, theratio of debt to GDP fell from 66 percent to 11 percent. What led to thechange? George Hall and Thomas Sargent (source below) computed thefollowing:

Interest Growth Primary Deficit(it − πt)Bt−1/Yt−1 −gtBt−1/Yt−1 Dt/Yt

1945-1974 –12.5 –21.6 –20.8

All numbers are percentages.

Answer. If you look at the numbers, they tell you that growth (the samedebt looked smaller when GDP grew) and primary surpluses account formost of this. You also see a negative contribution from real interestpayments. What does this tell us? With hindsight, we would say thatinvestors lost money in real terms because inflation was higher than theyexpected when they purchased government debt. If the government hadpaid (say) a one percent real return, this contribution would have beenpositive and the 1974 debt level would have been higher. In that sense,the US used inflation to reduce the debt burden.


It’s too technical for this course, but some of the material on debt dynamicswas adapted from Craig Burnside, ed., Fiscal Sustainability in Theory andPractice, World Bank, 2005.

More user-friendly (and very good) is George Hall’s summary of his workwith Thomas Sargent, “How will we pay down the debt?” They describesources of changes in the US debt position from World War II to 2008.

Most sources of macroeconomic data include the debt, the deficit, and theprimary deficit. One of the best sources of data and analysis is the IMF.Their World Economic Outlook database is updated twice a year. Theirhistorical database covers the last 200 years or more. Search: “imf debtdatabase.” And their Fiscal Monitor describes the fiscal situations in manycountries around the world.

One thing to keep in mind: reported debt numbers, whether from the IMFor other source, are generally inconsistent with reported deficits. It’s anembarrassment, to be sure, but true. In our examples, we construct (total)deficits from year-to-year changes in debt. If you ever need to know moreabout this, get in touch.

http://www.brandeis.edu/global/about/centers/rosenberg/repec/wpapers/Global_Finance_Brief_Hall.pdf

http://www.imf.org/external/pubs/cat/longres.cfm?sk=24332.0

http://www.imf.org/external/pubs/ft/fm/2013/01/fmindex.htm




Symbol Definition

G Government purchases of goods and servicesV TransfersB Stock of government debtT Tax revenues (not a tax rate)D Primary deficit (= G+ V − T )i Nominal interest rateg Discretely-compounded growth rate of real GDPπ Inflation rateg + π Discretely-compounded growth rate of nominal GDPY Nominal GDP

Note: In this chapter we have dealt only with nominal variables.


Variable Source

Federal government debt GFDEBTNFederal government debt held by the public FYGFDPUNFederal government net surplus FGDEFFederal interest outlays FYOINTNominal GDP GDPReal GDP GDPC1GDP deflator GDPDEF

To retrieve the data online, add the identifier from the source column to http://

research.stlouisfed.org/fred2/series/. For example, to retrieve real GDP,point your browser to http://research.stlouisfed.org/fred2/series/GDPC1




18International Capital Flows

Tools: Balance of international payments; dynamics of net foreign assets.

Key Words: Trade balance; net exports; current account; capital account;capital flows; net foreign assets.

Big Ideas:

• A current account deficit implies that a country is borrowing from therest of the world; we refer to this as a capital inflow. A current accountsurplus — a capital outflow — implies that a country is lending to therest of the world.

• A capital inflow (borrowing) can lead to problems if it does not supportproductive activities. For this reason, analysts often focus on the reasonsfor capital flows as well as their magnitude.

• The dynamics of net foreign assets are analogous to government debtdynamics.

International trade in goods and assets are at all-time highs all over theworld. In these notes, we describe the measurement system used to tracksuch trades: the balance of payments (BOP), a close relative of the NationalIncome and Product Accounts (NIPA) focusing on international transac-tions. This is simply accounting, in the sense that we’re counting thingsin a consistent way and not applying any particular theoretical framework.Nevertheless, an important idea emerges: Countries that run trade deficitscan also be thought of as attracting foreign investment or borrowing fromabroad. This connection between flows of goods and flows of assets gives usa new perspective on issues such as persistent trade deficits.

231


18.1 Trade in goods, services, and income

The balance of payments starts with a measurement system for trade ingoods and services and related flows of income. See Table 18.1.

Two closely-related measures are commonly reported. The merchandisetrade balance is similar to net exports, but includes only trade in goods(“merchandise”). It is reported monthly, and so is more readily availablethan the quarterly NIPA data, which are broader. Service trade includessuch things as foreign tourists visiting the US (hotels, restaurants), consult-ing services provided by US firms for foreign clients, and foreign studentsattending US universities. Since the US currently runs a modest surplus inservice trade, the merchandise trade deficit (slightly) overstates the deficitfor trade in goods and services (net exports). The current account balanceis a broader concept than net exports; it consists of net exports plus netreceipts of capital income, labor income, taxes, and transfers from abroad(net foreign income for short). Mathematically,

CA = NX + Net Foreign Income,

where CA is the current account and NX is (still) net exports.

Net foreign income includes such items as payment of interest on US gov-ernment bonds owned by foreign central banks (a negative entry), salariesreceived by American consultants working in Tokyo (a positive entry), andsalaries paid to Russian hockey players in the US (a negative entry). We see

Table 18.1: US balance of payments.

Net Exports of Goods and Services −508.3Net Labor Income from ROW −9.4Net Capital Income from ROW 247.4Unilateral Current Transfers from ROW −119.2Current and Capital Account −389.6

Net direct investment in US −225.4Net Purchase of Securities 167.0Net loans and other 243.7Financial derivatives 54.4Financial Account (inflows) 239.6

Statistical Discrepancy 149.9

The numbers are for 2014, billions of US dollars. ROW means “rest ofworld.” There are modest differences between these balance of paymentsmeasures and quarterly NIPA measures.

18. International Capital Flows 233

in Table 18.1 that the US was a net recipient of capital income and a netpayer of labor income.

The current account balance is, thus, the broadest measure of a country’sflow of “current” payments to and from the rest of the world. In the US, thedifference between net exports and the current account usually is modest.In other countries, the flows of labor and capital income may play largerroles.

18.2 Trade in assets

There are also flows related to capital and financial transactions. You cansee in Table 18.1 that the US in 2012 was the net recipient of $446.3b ofcapital and financial “inflows,” meaning that foreigners’ purchases of USassets were greater than US nationals’ purchases of foreign assets by thisamount. By convention, this is reported as a positive entry, even thoughit corresponds to an accumulation of liabilities with respect to the rest ofthe world. Foreigners’ purchases of domestic assets consisted of direct in-vestment (a controlling interest in a US business); purchases of equity andbonds issued by US corporations; purchases of US government and agencyissues; loans to US borrowers; and some other minor items we won’t botherto enumerate.

The central insight we gain from the balance of payments is that these assettransactions must match the current transactions:

Current Account + Capital and Financial Account = 0.

It’s not quite true in the data, because the numbers are not entirely ac-curate. We add a balancing item (“statistical discrepancy” or “errors andomissions”) to make up the difference. The point is that any deficit inthe current account must be financed by a capital inflow: selling assets oraccumulating liabilities with respect to the rest of the world. The sameaccounting truism applies to a firm or an individual. If your expendituresexceed your receipts, you need to sell assets or borrow to finance the differ-ence. Firms do this regularly when they make major additions to plant andequipment. And households often do the same when they buy houses.

The interesting thing about this accounting identity is that it gives us adifferent perspective on current account deficits. If we run a current accountdeficit as a reflection of a trade deficit, as in the US right now, we’re temptedto look at imports and exports as the reason. Perhaps foreign countriesare keeping our goods out of their home markets, or pushing down theirexchange rates to encourage exports. That’s the first reaction most people


have. But now we know that a current account deficit must correspond toa capital and financial inflow: Foreign investors are buying our assets. Thisperspective leads us to think about the investment opportunities in the USand elsewhere in the world that might lead to this. Are US assets particularlyattractive? Or are foreign assets unattractive? Both perspectives are right,in the sense that they’re true as a matter of accounting arithmetic, but thesecond one captures more clearly the dynamic aspect of decisions to invest.

18.3 Net foreign assets

The capital and financial account measures net flows of financial claims:changes in asset position, in other words. The balance-sheet position of aneconomy is referred to as its net international investment position (NIIP)or, simply, net foreign assets (NFA). If a country’s claims on the rest of theworld exceed their claims on it, then it has positive net foreign assets andis said to be a net creditor. If negative, a net debtor. The position changesover time, as indicated by the capital and financial account. Mathematically,we would say

NFAt = NFAt−1 + NX t

+ Net Foreign Income + Asset Revaluations. (18.1)

As in most accounting frameworks, there’s a connection between the incomestatement (the “flows” in economics parlance) and the balance sheet (the“stocks”).

An analogous relation for an individual might go something like this: Sup-pose you start with no assets or liabilities and then borrow 50,000 for thefirst year of your MBA. You spend the entire 50,000 and have no other sourceof funds, so you have a cash-flow deficit of −50, 000 for the year. At the endof the year, you have a net asset position of −50, 000. The bookkeeping isanalogous to equation (18.1), with NFA analogous to your net worth, NXanalogous to your annual cash-flow surplus or deficit, and the last two termsignored to keep things manageable. If we added interest on the debt, thatwould show up in Net Foreign Income.

Why do we need asset revaluations? By tradition, we measure internationalinvestments at market value, so if the value of an asset changes, we need toaccount for it in NFA. In international investments, asset revaluations occurboth through the usual change in prices of equity and bonds and throughchanges in exchange rates for instruments denominated in foreign currencies.

We report recent numbers for the US in Table 18.2. There we see that theUS has a net financial asset position of –$7,019.7b, meaning that foreign


Table 18.2: US net international investment position.

US-owned assets abroad 24,595.5Direct investment 7,124.0Corporate equity 6,719.7Bonds 2,852.8Loans and other 4,240.2Reserves & govt 434.3Financial Derivatives 3,224.5

Foreign-owned assets in the US 31,615.2Direct investment 6,228.8Corporate equity 6,665.2Corporate bonds 4,095.8US govt (treasuries, currency, official) 6,156.2Loans and other 5,318.6Financial Derivatives 3,150.7

Net international investment position −7,019.7

The numbers are for 2014 yearend, billions of US dollars.

claims on the US exceed US claims on the rest of the world by this amount.The table gives a complete accounting of these positions.

18.4 Sources of external deficits

We’ll talk more about the difference between the trade balance and the cur-rent account shortly, but for now, let’s ignore the difference and consider atrade deficit. If we have a large deficit, should we be worried? Is it a signthat the economy is in trouble? In this and many other cases, it’s helpful toconsider an analogous situation for a firm. Suppose that a firm is accumu-lating liabilities. Is that a bad sign? The answer is that it depends what theliabilities are used to finance. If they finance productive investments, thenthere should be no difficulty servicing the liabilities. In fact, the ability tofinance them suggests that someone thinks the investments will pay off. Butif the money is wasted (surely you can think of examples!), then investorsmight be concerned. The same is true of countries — it depends where thefunds go.

Consider the flow identity that we saw in Chapter 2:

S = Y − C −G = I + NX .

Typically, this is expressed as a ratio to GDP, with everything measured at


current prices:S

Y=

(1− C +G

Y

)=

I

Y+

NX

Y.

If we run a trade deficit (NX < 0), it must (as a matter of accounting )reflect some combination of low saving and high investment (high I). If weborrow from abroad to finance new plant and equipment, and the plant andequipment lead to higher output, we can use the extra output to cover theliabilities. If the investment is ill-considered, then we face the same issue asa firm in a similar situation.

What if we finance household consumption or government purchases? Wehave to answer the same question: Was the expenditure worthwhile? Herethere is room for concern, but a serious answer would depend on the natureof the expenditures.

The Lawson Doctrine, named after British government official Nigel Lawson,makes a distinction between public and private sources of deficits. Recallthat we can divide saving into private and government components, so that

Sp + Sg = I + NX .

In Lawson’s view, a trade (or current account) deficit that financed a dif-ference between private saving and investment is fine. But if the externaldeficit (trade or current account) stems from a government deficit, it’s wortha more careful look. In practice, emerging market crises often stem fromgovernment deficits that are financed abroad.

18.5 Debt dynamics and sustainability

The net foreign asset position evolves through time, just as governmentdebt does. As with government debt, the focus is traditionally on the ratioto GDP, which can change through either the numerator or denominator.We’ve seen that NFA changes like this:

NFAt = NFAt−1 + NX t + Net Foreign Interest Income

= (1 + it)NFAt−1 + NX t.

Note that everything here is nominal, including the interest rate it on thenet foreign asset position. Here, we’re skipping asset revaluations and thenon-interest component of net foreign income, but we could add them backin later if we thought they were relevant. If the growth rate of nominal GDPis gt + πt, we can write

Yt = (1 + gt + πt)Yt−1.


With these inputs, we see that NX /Y evolves like this:

NFAt

Yt≈ NFAt−1

Yt−1+ (it − πt)

NFAt−1

Yt−1− gt

NFAt−1

Yt−1+

NX t

Yt. (18.2)

The logic is identical to our analysis of government debt in equation (17.6).

How does the ratio of NFA to GDP change over time? The first issue iswhat real interest rate it − πt we pay on our borrowing. Typically therate is positive, which tends to increase a positive net foreign asset anddecrease a negative one. The second issue of real GDP growth gt. Highgrowth reduces the ratio of net foreign assets to GDP by increasing thedenominator. Finally, a trade surplus or deficit carries over directly to thenet foreign asset position.

If a country has a large current account deficit and a large and growing netforeign liability position, it’s sometimes said to be unsustainable. But if it’sunsustainable, what happens? The theory doesn’t say, but we can imaginesome possibilities: The trade deficit turns to surplus; the country defaults onsome or all of its foreign liabilities; and so on. More commonly, this is usedto project the growth of NFA over the next few years. If this leads to a largeratio of NFA to GDP, then investors may start to wonder whether they’ll berepaid. How large does it have to be to generate concern? It depends on thecountry and its institutions — just as we learned in studying governmentdebt in Chapter 17.

History tells us, however, that we see deficits and net liabilities in bothcountries on the brink of trouble (Argentina in the late 1990s) and countriesthat are performing well (Australia over most of its history). Most analystswould check further and find out what the deficit was financing (plant andequipment or government spending) and how it was structured (debt orequity). If debt, then the maturity and denomination are also relevant.

18.6 Big picture

The bottom line is that the current account deficit and net foreign assetposition are important indicators of the state of an economy. Important,yes, but it’s not always clear what to make of them. Take a current accountdeficit. Is a deficit is bad (it sounds bad!) or good (look, people want toinvest in our country!)? We need to look at the overall picture and come upwith a judgment. It’s another piece of the puzzle to consider when decidingwhether a country is a good opportunity.


Executive summary

1. There are several measures of current transactions with other countries:

• The merchandise trade balance measures exports minus imports ofgoods.

• Net exports includes trade in services, as well.

• The current account includes net international factor income, taxes,and transfers.

We refer to them collectively as “external” balances (deficits or surpluses).

2. The current account is mirrored by an equal and opposite capital andfinancial account measuring net asset transactions.

3. The net international investment position measures our current net claimson the rest of the world.

4. The flow identity tells us that the external deficit reflects some combina-tion of personal saving, government saving, and investment.


For more information:

• In the US, international transactions are reported along with the NationalIncome and Product Accounts by the Bureau of Economic Analysis. Seetheir International Economic Accounts.

• The International Monetary Fund’s International Financial Statistics isthe best single source of balance of payments and international investmentdata.

• International standards for BOP data are set by a working committeeof the International Monetary Fund. Their web site includes discussionsof both conceptual and measurement issues. The annual reports are agood overview. One of the recent highlights: In 2007, the world tradebalance was $108b, meaning that countries reported $108b more exportsthan imports. Since every export must be someone else’s import, thiscan’t really be true, but it points to some of the difficult measurementissues faced by the people putting these accounts together.

http://www.bea.gov/bea/di1.htm

http://elibrary-data.imf.org/finddatareports.aspx?d=33061&e=169393

http://www.imf.org/external/np/sta/bop/bop.htm

http://www.imf.org/external/bopage/arindex.htm



Table 18.3: Chapter 18 symbol table.

Symbol Definition

CA Current AccountNX Net exportsNFA Net foreign assetsS SavingY Gross domestic product (= Expenditure = Income)C Private consumptionI Private investmentG Government purchases of goods and services (not transfers)Sp Private saving (= Y − T − C)Sg Government saving (= T −G)i Interest rate on net foreign assetsg Discrete compound growth rate of GDP

In this chapter, we have dealt only with nominal variables.

Data used in this chapter

Table 18.4: Chapter 18 data table.

Variable Source

Current Account (BOP) BOPBCACurrent Account (NIPA) NETFINet exports of goods and services (NIPA) NETEXPNominal GDP GDPForeign-owned assets in US (+ equals increase) BOPIU.S.-owned assets abroad (+ equals decrease) BOPOAIncome payments (total) BOPMITIncome payments on foreign assets in US BOPMIAIncome receipts (total) BOPXRTIncome receipts on assets abroad BOPXRStatistical discrepancy (BOP) BOPERR


//research.stlouisfed.org/fred2/series/. For example, to retrieve the GDP,point your browser to http://research.stlouisfed.org/fred2/series/GDP





19Exchange-Rate Fluctuations

Tools: Arbitrage arguments.

Key Words: Real and nominal exchange rates; spot and forward exchangerates; purchasing power parity; covered/uncovered interest parity; the carrytrade.

Big Ideas:

• Exchange rates: where sensible theory comes to die. Meaning: short-runmovements in exchange rates are both hard to predict and hard to explainafter the fact.

• Purchasing power parity relates the relative price of goods across countriesto exchange rates.

• Interest rate parity (covered, uncovered) relates interest rates to exchangerates.

• The empirical performance of purchasing power parity and uncovered in-terest parity is poor.

Exchange rates (prices of foreign currency) are a central element of mostinternational transactions. When Heineken sells beer in the US, its europrofits depend on its euro costs of production, its dollar revenues in theUS, and the dollar-euro exchange rate. When a Tokyo resident purchases adollar-denominated asset, her return (in yen) depends on the asset’s dollaryield and the change in the dollar-yen exchange rate. Exchange rates, then,are an essential component of virtually all international transactions.

241


Nevertheless, countries in which exchange rates are determined in open mar-kets find that short-term fluctuations are substantial, largely unpredictable,and hard to explain after the fact. That’s been horribly disappointing tothose of us who would like to understand them better, but it’s a fact of life.From a business perspective, they’re a source of random noise. Heinekenprofits, for example, vary with the dollar-euro rate, even if the underlyingbusiness doesn’t change.

What follows is a summary of what we know.

19.1 Terminology

There is a lot of jargon associated with this subject. You’ll run acrossreferences to:

• Exchange-rate conventions. We typically express exchange rates aslocal currency prices of one unit of foreign currency. In the US, we mightrefer to the dollar price of one euro. In currency markets, the conventionsvary (every currency pair has its own), but we’ll try to stick with this one.It has the somewhat strange feature that an increase in the exchange rateis a decline in the relative value of the home currency. Of course, it’salso an increase in the value of the foreign currency. As a rule of thumb,remember that we quote prices in dollars (or whatever our local currencyis).

• Exchange-rate changes. Changes in exchange rates also have their ownnames. For a flexible exchange rate, we refer to a decrease in the value ofa currency as a depreciation and an increase as an appreciation. For afixed exchange rate, where the changes reflect policy, the analogous termsare devaluation and revaluation .

• Real exchange rates. You’ll see this term, too, but what does it mean?(What’s an imaginary exchange rate?) A nominal exchange rate is therelative price of two currencies: the number of units of currency A neededto buy one unit of currency B. The real exchange rate is the relative priceof a commodity or a basket of goods. If P is the US CPI in dollars, P ∗

is the European CPI in euros, and e is the dollar price of one euro (thenominal exchange rate), then the (CPI-based) real exchange rate betweenthe US and the Euro Zone is

RER = eP ∗/P,

the ratio of the price of EU goods to US goods, with both expressed in thesame units (here, dollars). We use an asterisk here and below to denotea foreign value.

19. Exchange-Rate Fluctuations 243

• Parity relations. We generally think that trade (“arbitrage”) will tendto reduce differences in prices and returns across countries. Parity rela-tions are based on the assumption that differences are eliminated alto-gether. It’s an extreme assumption, to be sure, but a useful benchmark.Purchasing power parity is the theory that prices of baskets of goods areequal across countries: P = eP ∗ (or RER = 1). This works for somespecific goods (think of gold), but anyone who takes a vacation abroadrealizes that it is, at best, a crude approximation for broad categories ofgoods (hotels, restaurant meals, or the CPI). Interest rate parity is theassumption that expected returns are equal for comparable investments indifferent currencies — think of US and Japanese treasury bills, or dollar-and yen-denominated eurocurrency deposits at major banks. Despite theglobalization of financial markets, this doesn’t work that well either.

We’ll see each of these in action shortly.

19.2 Properties of exchange rates

Flexible exchange rates move around — a lot. The standard deviation ofannual rates of change of currency prices is ten to 12 percent for major cur-rencies, more for emerging markets. That’s less than the standard deviationof equity returns (the return on the S&P 500 index has an annual standarddeviation of 16-18 percent) but a significant source of risk. With a stan-dard deviation of 10 percent, and assuming that changes in currency pricesare normally distributed, there’s a five-percent chance of seeing a one-yearchange greater than 20 percent either up or down.

You can get a sense of recent dollar movements from Figure 19.1, whichplots the price of one dollar expressed in Australian dollars, British pounds,euros, yen, and yuan/renminbi, respectively. (Inverses of dollar exchangerates, in other words.) They are constructed as indexes, with the January2001 values set equal to 100. You can see that the dollar-euro rate fluctuatesquite a bit; over the last five years, it’s ranged from 50 to 110. This reflects,to a large extent, the approaches taken by the US and the European centralbanks: They let their currencies float freely. The yen and the Australiandollar are similar. The renminbi, however, is fixed (or close to it) by theChinese central bank at a value of about eight yuan per dollar. More onthis in the next chapter.

19.3 Purchasing-power parity

So we’ve seen that exchange rates move around. But can we say anythingabout why? We can’t say much about short-term movements, but here’s a


Figure 19.1: The US dollar against other major currencies.

Yen

Aus. dollar

Euro

Yuan

4060

8010

012

0

Jan

uary

200

1 =

100

2001m1 2003m1 2005m1 2007m1 2009m1 2011m1 2013m1 2015m1

theory that gives us a long-term anchor for the real exchange rate. It’s ahelpful benchmark.

The idea is to compare prices of goods. Suppose that exchange rates adjustedto equate prices across countries. The logic is arbitrage: If a good is cheaperin one country than in another, then people would buy in the cheap countryand sell in the other, taking a profit along the way. This process will tendto eliminate the difference in prices, either through changes in the exchangerate or in the prices themselves.

Consider wine. Suppose that a bottle of (some specific) wine costs p = 26dollars in New York, and p∗ = 20 euros in Paris. Are the prices the same? Ifthe exchange rate is e = 1.3 dollars per euro, then the New York and Parisprices are the same once we express them in the same units. More generally,we might say that

p = ep∗.

We refer to this relation as the law of one price : that a product shouldsell for the same price in two locations. An even better example might begold, which sells for pretty much the same price in New York, London, andTokyo.

If the law of one price works for some products, there are many more forwhich restrictions on trade (tariffs or quotas), transportation costs, or other


“frictions” prevent arbitrage. Agricultural products, for example, are pro-tected in many countries, leading to substantial differences across countriesin the prices of such basic commodities as rice, wheat, and sugar. Cementfaces substantial shipping costs, even within countries. Many services (hair-cuts, dry cleaning, medical and legal services) are inherently difficult totrade, and often protected by regulation, as well.

The Economist , with its usual flair for combining insight with entertainment,computes dollar prices of the Big Mac around the world. The idea is thatit’s the same product everywhere, so differences in prices reflect deviationsfrom the law of one price. In July 2014, Big Mac prices were $4.80 in theUS, $4.95 in the Euro Zone, $3.64 in Japan, $2.57 in Argentina, and $2.73in China. These price differences vary widely over time. For example, InJanuary 2006, Big Mac prices were $3.15 in the US, $3.55 in the Euro Zone,$2.19 in Japan, $2.50 in Argentina, and $2.45 in China. Perhaps it’s nosurprise that the law of one price doesn’t hold — you can imagine the messinvolved in trying to arbitrage price differences. But it’s a good illustrationof international price differences more generally.

Despite such modest encouragement, the first-cut theory of exchange rates isbased on an application of law-of-one-price logic to broad baskets of goods.The so-called theory of purchasing power parity (PPP) is that local andforeign price indexes (P and P ∗, say) are linked through the exchange rate:P ≈ eP ∗ or

RER = eP ∗/P ≈ 1. (19.1)

The approximation symbol suggests that we don’t expect this to be perfect.In the most common applications, the price indexes are CPIs (consumerprice indexes), and we refer to the measure of the real exchange rate asCPI-based. If this doesn’t work for specific goods, why might we expectit to hold for average prices of goods? One reason is that, for any pair ofcountries, we might see as many products that are “overpriced” as there areproducts that are “underpriced.” When we average, these deviations couldoffset each other, but, in fact, they don’t. If prices of some goods are cheaperabroad, then prices of other goods tend to be, too.

What limited success we have comes in the long run. As an empirical matter,deviations from PPP tend to average out over time. Sometimes prices arehigher in Paris, sometimes higher in New York, but, on average, prices areroughly comparable. Prices are lower, on average, in countries with lowerGDP per capita, but here, too, large fluctuations in the real exchange ratetend to disappear with time. How much time do we need for this to work?At least several years. If you’re thinking of going to Paris next month,


there’s little reason to expect that we’ll be closer to PPP by then. Maybewe will, maybe we won’t; it’s a tossup.

Real exchange rates computed this way are often used to judge whether acurrency’s price is reasonable. If the prices are lower at home than abroad(RER > 1), we say the (home) currency is undervalued . If prices are higherat home (RER < 1), we say the currency is overvalued . Over- and under-valued here means relative to our theory of PPP. We can do the same thingwith the Big Mac index. We saw earlier that Big Macs were cheaper inChina than in the US, so we might say that the dollar is overvalued relativeto the yuan. Over time, we might expect most of these “misvaluations” todecline. Experience suggests, however, that any such adjustment will takemany years. Our best estimates are that about half the difference fromPPP will disappear in five years. We can do the same thing with CPIs, withone difference: Since CPI are indexes, we don’t know the absolute prices.The standard approach is to find the mean value of the real exchange rate(or its logarithm) and judge under- or overvaluation by comparing the realexchange rate to its mean, rather than one.

19.4 Depreciation and inflation

We can express the same theory in growth rates, with the result that thechange in the exchange rate (the depreciation of the currency) should equalthe difference in the two inflation rates. Simply put, if one country has ahigher inflation rate than another, then we would expect its currency to fallin value by the difference. That’s not true over short periods of time, but it’sreasonable guide over longer periods of time. Countries with high inflationrates find that their currencies fall in value as a result.

Here’s how that works. The PPP relation equation (19.1), implies that

et = Pt/P∗t .

(Feel free to put ≈ here if you prefer.) If we take (natural) logs of bothsides, we have

ln et = lnPt − lnP ∗t .

If we take the same equation at two different dates, we have

ln et+1 − ln et = (lnPt+1 − lnPt)− (lnP ∗t+1 − lnP ∗t )

= πt+1 − π∗t+1.

In words: The depreciation rate equals the difference in the inflation rates.It’s simply PPP in growth rates.


Does this work? It’s pretty good for long-run averages (five to ten years ormore), but like everything we know about exchange rates, not very usefulfor short-term movements outside very very-high-inflation situations.

Figure 19.2: Venezuelan depreciation and inflation differential.

Exchange rate depreciation

Inflationdifferential

020

4060

8010

0

Rat

e (p

erce

nt)

1985m1 1990m1 1995m1 2000m1 2005m1

By way of example, consider the exchange rate between the Venezuelan Boli-var and the US dollar. Between January 1985 and January 2006, Venezuela’saverage annual inflation rate was 30 percent, as opposed to the US’s 2.9 per-cent. In the same period, the Bolivar depreciated at the average yearly rateof 27.9 percent, i.e. only .8 percent more than implied by the PPP condition.In the short run, however, deviations from PPP are the norm. Figure 19.2shows that this has definitely been the case for the Bolivar: There havebeen plenty of periods in which exchange-rate depreciation did not closelytrack the inflation differential with the United States. In some instances, inparticular in the late 1980s, the deviations were due to the central bank’sattempt to keep the exchange rate constant. In other cases (the early 1990s,for example), the deviations probably had nothing to do with central bankinterventions.

In developed countries, it’s not unusual to see deviations of the real exchangerate from one of 30-40 percent in either direction. Figure 19.3 shows thisfor the dollar-euro. This picture is typical of developed countries: Inflationdifferentials are relatively small, so changes in the real and nominal exchangerates are almost equal. These deviations from PPP tend to disappear withtime, but, as we saw earlier, they go away slowly.


Figure 19.3: Dollar versus euro and inflation differential.

Inflationdifferential

Exchange rate depreciation

-30

-20

-10

010

20

Rat

e (p

erce

nt)

2000m1 2005m1 2010m1 2015m1

19.5 Interest rate parity and the carry trade

Exchange rates also play a role in interest rate differences across countries.In June 2004, for example, three-month eurodollar deposits paid interestrates of 1.40 percent in US dollars, 4.78 percent in British pounds, 5.48percent in Australian dollars, and 2.12 percent in euros. If internationalcapital markets are so closely connected, why do we see such differences?The answer is that these returns are expressed in different currencies, sothey’re not directly comparable.

Let’s think about how prices of currencies show up in interest rate differen-tials. We’ll start with a relation called covered interest parity, which saysthat interest rates denominated in different currencies are the same once you“cover” yourself against possible currency changes. The argument followsthe standard logic of arbitrage used endlessly in finance. Let’s compare twoequivalent strategies for investing one US dollar for three months. The firststrategy is to invest one dollar in a three-month eurodollar deposit (withthe stress on “dollar”). After three months, that leaves us with (1 + i/4)dollars, where i is the dollar rate of interest expressed as an annual rate.

What if we invested one dollar in euro-denominated instruments? Here weneed several steps to express the return in dollars and make it comparableto the first strategy. Step one is to convert the dollar to euros, leaving uswith 1/e euros (e is the spot exchange rate — the dollar price of one euro).


Step two is to invest this money in a three-month euro deposit, earningthe annualized rate of return i∗. That leaves us with (1 + i∗/4)/e eurosafter three months. We could convert it at the spot rate prevailing threemonths from now, but that exposes us to the risk that the euro will fall. Analternative is to sell euros forward at price f . In three months, we will have(1 + i∗/4)/e euros that we want to convert back to dollars. With a three-month forward contract, we arrange now to convert them at the forwardrate f expressed, like e, as dollars per euro. This strategy leaves us with(1 + i∗/4)f/e dollars after three months.

Thus, we have two relatively riskless strategies, one yielding (1 + i/4), theother yielding (1 + i∗/4)f/e. Which is better? Well, if either strategy hada higher payoff, you could short one and go long on the other, earning extrainterest with no risk. Arbitrage will tend to drive the two together:

(1 + i/4) = (1 + i∗/4)f/e. (19.2)

We call (19.2) covered interest parity . Currency traders assure us that cov-ered interest parity is an extremely good approximation in the data, exceptin extreme periods of liquidity, such as a financial crisis. The only differencebetween the left and right sides is a bid-ask spread, which averages less than0.05 percent for major currencies.

A related issue is whether international differences in interest rates reflectdifferences in expected depreciation rates. Does the high rate on Aussiedollars (AUD) reflect the market’s assessment that the AUD will fall invalue relative to (say) the euro? To see how this works, suppose that weconverted the proceeds of our foreign investment back to local currency atthe exchange rate prevailing in three months. Our return would then be

(1 + i∗/4)e3/e,

where e3 is the spot exchange rate three months in the future. This invest-ment is risky, since we don’t know what the future exchange rate will be, butwe might expect it to have a similar expected return to a local investment.That is,

(1 + i/4) = (1 + i∗/4)E(e3)/e, (19.3)

where E(e3) is our current expectation of the exchange rate in three months.This relation is an application of the expectations hypothesis to currencyprices (the forward rate equals the expected future spot rate) that is com-monly referred to as uncovered interest parity .

In fact, uncovered interest rate parity doesn’t work. It implies that high-interest-rate currencies depreciate, when, in fact, they appreciate (increasein value) on average, making them potentially good (if risky) investments.


If i > i∗, we invest at home. If i < i∗, we invest abroad, expecting topocket not only the higher interest rate but an appreciation of the currency(e3 > e). That’s the essence of what is called the “carry trade.” Why this in-vestment opportunity persists remains something of a mystery to academicsand investors alike.

Two fine points: (i) This feature of the data does not apply to the currenciesof developing countries, where higher interest rates typically do imply fu-ture depreciation. That is, uncovered interest parity works better here. (ii)In developed countries, forecasts of exchange-rate changes based on interestdifferentials have an R2 of 0.05 or less. That’s still useful for investmentpurposes, but leaves most of the variance of exchange-rate changes unex-plained.

19.6 Predicting exchange rates

Let’s summarize what we’ve learned about movements in exchange rates:

• PPP works reasonably well over long periods of time, but has little em-pirical content over periods of less than a few years, and virtually noneover periods under a year.

• Interest rate differentials have some forecasting power, with high-interest-rate currency increasing in value, on average, but they leave most of thevariance of exchange-rate movements unexplained.

Can we do better than this? A little, but probably no more than that. It’sextremely hard to forecast exchange rates better than a 50-50 bet on up ordown. Interest differentials do a little better, but only a little. We may beable to do better still using more complex theory or personal judgment aboutpolicy, but years of failure suggest that it’s very hard to beat a random walkconsistently.

Executive summary

1. In the long run, exchange rates tend to equalize prices of products acrosscountries (PPP).

2. In the short run, exchange-rate movements are large and unpredictable.


Review questions

1. Purchasing power parity for Big Macs. The Economist reports the fol-lowing data for local prices of Big Macs and US dollars in July 2011:

Big Mac Price Exchange Rate(Local Currency) (LCUs per Dollar)

(A) (B)

Argentina 20.0 4.13Brazil 9.50 1.54India 84.0 44.4United States 4.07 1.00

LCUs are “local currency units.”

(a) What is the dollar price of a Big Mac in each of these locations?

(b) In what ways is the ratio of USD Big Mac prices similar to the realexchange rate?

(c) What exchange rates for the first three currencies would equate thedollar prices of Big Macs in other countries to the US price? How isthis related to PPP?

(d) How much are the first three currencies over or undervalued relativeto the US dollar?

Answer. The calculations are summarized in

Big Mac Big Mac Overvaluation(USD) (Ratio) (percent)

(C) (D) (E)

Argentina 4.84 4.91 19Brazil 6.17 2.33 51India 1.89 20.64 −53United States 4.07 1.00 0.0

(a) Dollar prices of Big Macs are reported above as column (C), com-puted as (A)/(B).

(b) The relative price of Big Macs is like a real exchange rate. The realexchange rate is the ratio of prices converted to a common currency:

RER = eP ∗/P.

Usually we use prices indexes for P and P ∗, here we use prices ofBig Macs.


(c) Mathematically, we set RER equal to one (the PPP condition) andsolve for e = P/P ∗. In the table, we computed this as the ratio ofentries on column (A) to the US entry in the same column. Thatgives us a PPP benchmark for what the exchange rate should be.

(d) If we compare our calculation of the PPP exchange rate in (c) tothe actual, we can see how far off we are. In the table, we compute“overvaluation” as the percentage difference between true exchangerates and our PPP calculation: 100*[(D)/(B)-1]. We see that theBrazilian real is overvalued (Big Macs are expensive there) and theIndian rupee is undervalued (Big Macs are cheap there).

2. Forecasting the euro. Suppose the euro is “overvalued” in PPP termsrelative to the dollar (goods are more expensive in Europe) and EuroZone short-term interest rates are slightly above US interest rates. Giventhese facts, how would you expect the euro/dollar exchange rate to changeover the next 6 months? 6 years? How good is each of these informedguesses?

Answer. Purchasing power parity is a long-run “anchor” for the exchangerate: if prices of goods and services in the Euro Zone are higher than thosein the US, when expressed in a common currency, we’d expect the euroto fall in value relative to the dollar — eventually. This is pretty muchuseless over a period as short as 6 months, but has some content over 6years. More useful in the short-run is the interest differential. Since theEuro interest rate is higher, we’d expect the euro to increase in value.Neither works well: an R2 of 0.05 would be good over periods of a fewmonths.


FRED has exchange rates for many countries. So does the Fed; search: “fedexchange rates.”

The Economist’s Big Mac index (search: “big mac index”) is the center ofa nice web site on exchange-rate data and issues.

Deutsche Bank’s Guide to Exchange-Rate Determination is a terrific sum-mary of what we know about exchange rates from a bond and currencytrader’s perspective.


http://www.federalreserve.gov/releases/h10/hist/

http://www.economist.com/content/big-mac-index




Symbol Definition

e Spot exchange rate = home currency price of foreign currencyf Forward exchange rateP Domestic price levelP ∗ Foreign price levelRER Real exchange rate = eP ∗/Pπ Domestic inflationπ∗ Foreign inflationi Domestic nominal interest ratei∗ Foreign nominal interest rateE(x) Expected value of a variable x


Variable Source

USD/euro exchange rate EXUSEUYuan/USD exchange rate EXCHUSYen/USD exchange rate EXJPUSUSD/UK pound exchange rate EXUSUKUSD/AUD exchange rate EXUSALVenezuela/USD exchange rate EXVZUSReal trade-weighted USD index (broad) TWEXBPAUS consumer price index CPIAUCSLEuro area harmonized consumer price index CP0000EZCCM086NEST


//research.stlouisfed.org/fred2/series/. For example, to retrieve the dollar-euroexchange rate, point your browser to http://research.stlouisfed.org/fred2/series/

EXUSEU



http://research.stlouisfed.org/fred2/series/EXUSEU

http://research.stlouisfed.org/fred2/series/EXUSEU


20Exchange-Rate Regimes

Tools: Central bank balance sheet.

Key Words: convertibility; capital mobility; capital controls; fixed andflexible exchange rates; foreign exchange reserves; sterilization.

Big Ideas:

• Countries adopt different exchange rate regimes: fixed, floating, and inbetween.

• The trilemma limits our policy options: we can choose only two of (i) fixedexchange rate, (ii) free flow of capital, and (iii) discretionary monetarypolicy.

• Fixed exchange-rate regimes must be defended through open market op-erations and are vulnerable to speculative attack.

The term “exchange-rate regimes” refers to the various arrangements thatgovernments around the world make about international transactions. We’llsee (i) how central banks intervene in currency markets to fix the price and(ii) how such fixed exchange-rate systems sometimes blow up.

20.1 A catalog of foreign-exchange arrangements

Governments follow a wide range of policies toward their currencies. Oneaspect of policy is whether people and businesses can freely exchange theirlocal currency for another: whether the currency is convertible. The USdollar, for example, is convertible. You can walk into most banks in New

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York and use dollars to buy dozens of foreign currencies. Or you can useyour credit card abroad and have the currency transaction done for you.The renminbi, however, has limited convertibility. You need approval fromthe Chinese central bank to buy or sell Chinese currency.

A related issue is capital controls: whether the government restricts move-ments of capital (funds) in and out of the country. In the US, capital isgenerally free to move in and out of the country, although there are restric-tions on foreign ownership of companies in some industries (banks, media,airlines). In China, there are limits on foreign investments that vary (asin the US) by industry and type (direct investment is easier than buyingsecurities). And there are restrictions that limit the amount of money thatChinese citizens can take out of the country. These controls are typicallyenforced through convertibility: since you can’t convert renminbi to (say)dollars, you can’t take it out of the country.

There’s nothing unusual about this. Many countries limit convertibility andcapital flows, particularly during times of stress. Malaysia imposed capitalcontrols during the Asian crisis of 1997, and Argentina did the same in 2002.

Another aspect of foreign-exchange policy is whether the price of the cur-rency is set by the government, allowed to float freely, or something inbetween. If the price is determined in a free market, we say that we have aflexible or floating exchange-rate regime. If the government sets the price,we say it has a fixed or pegged exchange-rate regime. A managed float issomewhere in between.

20.2 Fixed exchange rates

Many countries have fixed exchange-rate regimes of one sort or other. Ecuadoruses US dollars, so its currency is fixed by design. The countries of the Eu-ropean Monetary Union use a common currency, the euro. Other countrieshave their own currencies, but intervene to fix the price. Probably the mostprominent current example is the Chinese renminbi, which has been quasi-fixed for more than a decade.

How does a central bank set the exchange rate if the currency is convertible?Can it simply announce a rate? Probably not. You can state a price, butyou can’t make people trade at it. You could claim, for example, that yourapartment is worth $10m, but if no one is willing to buy it for that price, thestatement is meaningless. For the same reason, a central bank must backup its claim to fix the exchange rate by buying and selling as much foreigncurrency as people want at the stated price.

20. Exchange-Rate Regimes 257

Let’s think through how this might work. Suppose the New York Citygovernment decided to fix the price of beer at $2 a six pack (cheap evenif you live outside NYC). It supports this price by buying or selling anyamount at the quoted price. Can they keep the price this low? Our guessis that at this price, beer makers would not find it profitable to make any(at least not any that we’d be willing to call beer). People would then floodthe government with requests for beer, which the government would not beable to meet. When the government reneged on its promise to buy or sell at$2, the price would rise above $2 to its market level, either officially or onthe black market. Unless the government has enough beer to back up theprice, the system will collapse. Alternatively, suppose that the governmentset the price at $20. Beer makers would flood the government with beerat this price, leaving the government with a huge surplus. This is roughlywhat Europeans do with agriculture, where artificially high prices have leftthe EU with “mountains of butter,” “lakes of wine,” and so on. The pointis that the government can fix a price only if it is willing and able to buyand sell at that price — or outlaws market transactions altogether.

The same logic applies to currencies. If the People’s Bank of China were tosupport an excessively high price for the renminbi, then it would be floodedwith offers from traders selling renminbi for (say) dollars. Its balance sheetwould look something like this:

Assets LiabilitiesFX Reserves 20 Money 200bonds 180

We made these numbers up, but they give us the right idea. The central bankhas the usual liabilities, “money” and government bonds , and also holdssome foreign currency reserves, which you might think of as dollars. ThePBOC intervenes in the currency market by trading renminbi for dollars,and vice versa, depending on market conditions.

Suppose, for example, that Nike wanted to convert $2m to renminbi to builda new plant in China. It would do this through a Chinese bank. If the bankhad no countervailing trades, it would go to the PBOC and exchange the$2m for renminbi at the going rate — say ten yuan per dollar, to make thearithmetic simple. The PBOC’s balance sheet would then show an increaseof 20m yuan worth of foreign currency and a comparable increase in itsmonetary base:



Note that the transaction doesn’t make the PBOC any richer. Its net worthis unchanged, since it has exchanged assets with equal value.

The difference, then, between fixed and flexible exchange-rate regimes isthat the former obligates the central bank to buy and sell currencies at thestated price.

20.3 Sterilization

You might have noticed that when a central bank buys and sells foreigncurrency, its money supply changes. In the example above, the purchaseof 20 worth of foreign currency increased the money supply by the sameamount. It’s automatic: when the central bank purchases foreign currency,it offers domestic currency in return.

Central banks often want to reverse this impact of foreign exchange inter-vention by engaging in an offsetting open market operation. We refer to thisas sterilization.

In our example, the central bank would like to reduce the money supplyby 20, offsetting the impact of buying foreign currency. It does so with anopen market sale of government bonds. The sale of bonds is paid for in localcurrency, which is now held by the central bank . Its balance sheet is now


In China’s case, this has happened to such an extent that the bond positionis negative: the PBOC is an issuer of bonds, not an investor.

20.4 The trilemma

Exchange-rate policy is, evidently, a dimension of monetary policy since itinvolves management of the central bank’s balance sheet. Is it another toola central bank can use to manage the economy?

Both logic and experience tell us that the central bank’s choices are limited.The sharpest example is the trilemma. You can choose, at most, two of thefollowing:


• fixed exchange rate

• free international flow of capital

• discretionary monetary policy

If you try for all three, something will give, probably the exchange rate.

The US lets the exchange rate float, which allows it to have a discretionarymonetary policy and free movements of capital. China limits the interna-tional flow of capital, which allows it to have a fixed exchange rate and somedegree of monetary policy discretion. The UK, in 1992, tried for all three,and it blew up, driving them out of the European Monetary System, theprecursor of the European Monetary Union.

20.5 Exchange-rate crises

As a matter of experience, fixed exchange-rate systems often collapse —sometimes spectacularly — when the central bank runs out of reserves.

We can illustrate the mechanics with the central bank’s balance sheet. Sup-pose that it looks like the one above, with “fx reserves” of 40. And suppose,further, that investors would like to exchange 50 worth of pesos for the samevalue in dollars. Once the central bank runs out of dollars, it can no longersupport the exchange rate, which becomes (more or less automatically) float-ing.

It’s the same issue we illustrated earlier with beer: If people would preferto buy foreign currency at the official exchange rate, and the currency isconvertible, the central bank may find that its supply of foreign reservesis not enough to meet the market demand. (The market for currencies isenormous, so you need a lot of reserves.) For that reason, currency tradersoften look closely at the central bank’s foreign currency reserves to measureits ability to maintain a fixed rate.

What invites “speculative attacks” on a currency with a fixed exchange rate?Often, it’s a problem of time consistency. A fixed exchange rate is a policypromise to exchange one currency for another at a specified price withoutlimit into the future. If investors today expect that a future policymakerwill alter that price, what will stop them from selling the “expensive” cur-rency today? In a foreign-exchange market that transacts about four trilliondollars daily, few governments have adequate foreign reserves to fend off arun on a fixed exchange rate.


One classic currency run occurred in 1992 in the United Kingdom. As partof the European Exchange Rate Mechanism (ERM), the UK had effectivelyfixed its currency, sterling, to Germany’s Deutsche Mark (DM). But Ger-many was in its post-unification economic boom and needed high interestrates to limit inflation, while the UK was in a deep recession and neededlow interest rates. Doubting that UK policymakers would keep interestrates high just to maintain the fixed exchange rate, speculators sold ster-ling. They made a fortune when the UK exited the ERM in September 1992and sterling plunged versus the DM.

You might ask: Should the UK have considered capital controls insteadof devaluing sterling? One practical obstacle was that any hint of controlswould have further encouraged investors to flee sterling before they could nolonger do so. Where time consistency is lacking — in this case, in currencypolicy — instability often follows.

There’s a big-picture question lurking behind the scenes here: whether fixedexchange rate regimes reduce volatility. With flexible rates, we tend to see alot of short-run volatility. With fixed exchange rates, short-run volatility islow most of the time, but we occasionally have spikes in volatility when thesystem collapses. Neither seems completely appealing, but that’s the choicewe’re given.

20.6 Strong fixes

The tendency for fixed exchange rates to blow up has led to two competinglines of thought. One is to let them float — let the pressure off, so to speak.The other is to reinforce the fixed-exchange-rate system and nail the liddown tighter. Nothing has proved foolproof to date, but you never know.

One way to reinforce a fixed exchange rate is with a currency board. Theidea is to start off with a large reserve of foreign currency and limit issuesof domestic currency to this amount. That way, you should not run out offoreign currency when people trade in their local currency. Argentina setup a system like this in the 1990s, and established an exchange rate of onedollar per peso. But it was dissolved in a currency crisis ten years later.Hong Kong has had such a system since 1983, with the Hong Kong dollarpegged to the US dollar. As a result, interest rates in Hong Kong mirrorthose in the US: it has, in a sense, inherited US monetary policy.

A more extreme arrangement is a common currency. EMU (the euro area)is the most ambitious effort along these lines to date. But it has been understress for years, and it remains unclear whether it will survive in its currentform.


Executive summary

1. “Convertibility” and “capital mobility” refer to policies limiting currencytransactions and international capital flows.

2. Foreign currency reserves are an indicator of the government’s ability tomaintain a fixed exchange rate.

3. The trilemma says you can have, at most, two of the following threethings: (i) fixed exchange rates; (ii) international capital mobility; and(iii) discretionary monetary policy.

Review questions

1. Foreign exchange market intervention. Use a hypothetical central bankbalance sheet to show how purchases of foreign currency affect the bank’sassets and liabilities. What does this purchase do to the supply of money(currency)?

Answer. When a central bank buys foreign currency, it receives it fromprivate owners and gives them domestic currency in return. The latteris an increase in the domestic money supply. Suppose, for example, thatthe central bank starts with the balance sheet


The purchase of 25 worth of foreign currency changes the balance sheetto


2. Sterilization. Suppose that the central bank has increased the moneysupply by purchasing foreign currency, as described above. How might itoffset this impact on the money supply (sterilize it, so to speak)?

Answer. It does an equal sale of bonds, accepting money in return. If itsells 25 worth of bonds, the balance sheet changes to



The net result of the two trades is that its liabilities are now more heav-ily weighted in foreign currency. If the foreign currency rises, it makesmoney; if it falls, it loses money. This posture is designed as protectionagainst a sharp fall in local currency (or rise in foreign currency), and itdoes that.

3. Hong Kong’s trilemma. Use the trilemma to explain why Hong Kong hasinherited US monetary policy.

Answer. Hong Kong has (i) a fixed exchange rate against the US dollarand (ii) international capital mobility. The trilemma then tells us that itcan’t have its own monetary policy. Should they want their own monetarypolicy, either (i) or (ii) has to go.


The International Monetary Fund’s Annual Report on Exchange Arrange-ments is the definitive guide to exchange-rate arrangements: fixed, flexible,capital controls, and so on.

21Macroeconomic Crises

Tools: Crisis triggers and indicators.

Key Words: Sovereign default; bank runs and panics; refinancing (rollover)risk; leverage; conditionality; solvency and liquidity.

Big Ideas:

• Common triggers of macroeconomic crises are sovereign debt problems,financial fragility, and fixed exchange rates.

• Measures related to these triggers can help identify countries in trouble:debt and deficits, financial weakness, exchange rate regime, and so on.

• The goals of crisis prevention and crisis management are often at odds.

Economies periodically experience crises: economic downturns that are notonly larger than typical recessions but qualitatively different. The ideais now fresh in our minds, but similar episodes have occurred throughoutrecorded history. They’re less common in modern, developed countries, butthey can happen anywhere. Like snowflakes and business cycles, no two areexactly the same, but they share some common features.

21.1 Classic crisis triggers

There are three classic triggers of macroeconomic crises: sovereign debt,financial fragility, and a fixed exchange rate.

Sovereign debt problems. If investors fear that a government may notrepay its debt, the market for debt collapses, often taking the economy with

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it. In the old days, wars were the standard problem. Wars are expensive,and if investors thought the expense was more than the government waswilling or able to bear, they would stop buying the debt. In modern times,governments spend money on many things besides wars, but the possibilityof default remains. Argentina in 2002 and Greece today are recent examples.These experiences remind us that sovereign debt need not be risk-free.

The central issue with government debts is sovereignty. If a corporation de-faults, the creditors take it to court and claim the assets. With governments,there’s no such mechanism, and the process is sloppier as a result.

Financial fragility. We know from centuries of experience that when thefinancial system freezes up, economic activity slows down sharply. We sawthat in 2008, but the same thing happened during the Bank of EnglandPanic of 1825, the Baring Crisis of 1890, the US Panic of 1907, Japan andScandinavia in the 1990s, and many other occasions. It’s a feature of evenadvanced financial systems that they sometimes break.

In most cases, these financial problems follow from poor investments (realestate is a common example), which put the solvency of financial institutionsin question. The problems tend to snowball: Worries about the viabilityof one firm may lead others to reduce their lending, leading to a cycle ofretrenchment that puts even sound firms in trouble. The word “panic” isapt here and stems from the imperfect information that investors have whendeciding where to put their money.

Fixed exchange rates. For whatever reason, fixed exchange rates peri-odically must be defended in ways that undermine the economy. Recentexamples include the UK in 1992, Mexico in 1994, Korea in 1997, and Ar-gentina in 2000.

Many crises combine several of these elements. The countries of the euroarea face all three. In Ireland and Spain, bailing out their banks landedthe governments in financial peril. In other countries, bank positions ingovernment debt or in overpriced real estate put the banking systems inperil. Finally, the common currency eliminates exchange rate changes as apossible correction mechanism.

21.2 Crisis indicators: the checklist

Crises are inherently hard to predict. Why? Think about cardiologists. Weunderstand that they can identify risk factors (weight, high blood pressure)but cannot predict the date of a heart attack with any precision. Crises are

21. Macroeconomic Crises 265

worse. Once people see a crisis on the way, their actions tend to reinforce it:they sell government debt, withdraw funds from banks, or shift their moneyto foreign currency. But like a cardiologist, we can use what we know toidentify signs of trouble.

Analysts differ in the details, but most would include the following in their“checklist” of crisis indicators:

Government debt and deficits. The primary issue here is the quality ofgovernance. That aside, common rules of thumb include: Worry if govern-ment deficit is more than 5 percent of GDP or debt is more than 50 percentof GDP. Adjust upward for developed countries, downward for developingcountries and for regional governments. And watch out for hidden liabili-ties: pensions, health care, bailouts, etc. These are often much larger thanofficial liabilities.

Fine points: Worry further if debt is short-term and/or denominated inforeign currency. Short-term debt subjects the government to refinancing(“rollover”) risk; markets may demand better terms or refuse to refinance.Foreign-denominated debt subjects government to risk if currency falls invalue, making the debt larger in local terms.

Banking/financial system. This isn’t something we’ve discussed, butanalysts track leverage, duration mismatch, exposure concentration, risk-management processes, and nonperforming loans. The challenge is measur-ing them accurately from reported information. Some of the most troublingsituations come with low-quality data.

Exchange rate and reserves. Rule of thumb: Worry if the exchange rateis fixed, or close to it, and the currency is significantly overvalued in PPPterms (Big Macs cost 30 percent more than in other currencies; the realexchange rate has risen more than 30 percent in the past 2-5 years). Worrymore if foreign-exchange reserves are low or have fallen significantly.

Political situation. Crises are often more political than economic. Coun-tries with effective governments suffer fewer crises and deal with those thatoccur more effectively. Analysts therefore look for signs that the politicalsystem is unable or unwilling to deal with problems that might turn intocrises. Zimbabwe’s hyperinflation and Argentina’s debt crisis are good ex-amples. Or the Weimar Republic in 1920s Germany.

All of these things generate more concern in countries with weak institutions.It’s not an accident that Greece is in worse trouble than France or Germany.


21.3 Crisis responses

What should a government do when faced with a crisis? It depends on thetrigger. Standard advice includes:

Sovereign debt crises. If the problem is that the government is borrowingtoo much, the answer is to stop doing it — run primary surpluses until thedebt is manageable. Default is also an option, and saves money in the shortterm, but probably raises borrowing costs in the future. And if you gothrough a default, it’s helpful to resolve it as quickly as possible.

IMF support is often used to cushion the blow: Contingent on progress withthe deficit, the IMF lends the government money on more attractive termsthan the market would provide. This “conditionality,” as it’s called, helpsreduce moral hazard (you get the money only if you behave) and providescover for local politicians (the IMF made us do this). Such conditionallending can be critical in a crisis, when high borrowing rates exacerbate thegovernment’s debt problems. (See: debt dynamics.)

Financial crises. If the financial system is fundamentally sound (solvent)but illiquid, the longstanding advice is for the central bank to lend aggres-sively. The classic quote comes from Walter Bagehot, a 19th-century busi-nessman and journalist: “To avert panic, central banks should lend earlyand freely, to solvent firms, against good collateral, and at high rates.”

If the financial system is insolvent, it’s important to get it recapitalizedand operating again. This advice comes with more than a little irony, asgovernments sometimes find themselves bailing out precisely those banksthat triggered the crisis. The trick is to do it in ways that inflict somepain on the bank’s management and creditors (incentives for the future)and don’t bankrupt the government. These things happen fast, so it’s hardto get everything right.

Fixed exchange rates. Let them float. A more controversial approachis to impose capital controls to inhibit the response of capital markets to apossible drop in the exchange rate. (See: trilemma.) capital controls area dangerous tool, because the fear of future capital controls can generate acrisis on its own, as investors rush to get their money out of the country.capital controls on inflows may, for that reason, be more attractive thancontrols on outflows.

Executive summary

1. The classic crisis triggers are (i) government debt and deficits, (ii) a fragilefinancial system, and (iii) a fixed exchange-rate system.


2. Crises are hard to predict, but we nevertheless have useful indicatorsconnected to each of the triggers.

3. Politics and institutions are central.

Review questions

1. Risk and opportunity in Ghana (May 2012). You have been asked to pre-pare a risk assessment for the West African country of Ghana. Ghana is aformer British colony that has been growing rapidly in recent years aftera period of unusually stable politics. The Economist Intelligence Unitrefers to it as a “robust democracy.” The World Economic Forum rankedGhana 114th (of 133) in their Global Competitiveness Report. They con-tinue: “The country continues to display strong public institutions andgovernance indicators, particularly in regional comparison.”

The EIU’s Country Risk Report adds:

• The December 2012 elections are expected to be close. The presi-dent, John Atta Mills, came to power promising accountability andtransparency, but has struggled to maintain party unity while evidenceemerges of financial impropriety of some government ministers.

• The victor faces a challenging policy environment, particularly the fis-cal situation.

• Expectations among the population are high as production starts atthe offshore Jubilee oil field.

• The government’s decision to allow use of 70% of future oil revenueas collateral for borrowing is a cause for concern if the revenue is notmanaged properly.

• The Bank of Ghana (the central bank ) faces the twin goals of contain-ing inflation and fostering growth.

• The currency — the cedi — floats with occasional heavy intervention.

Your mission is to assess the risks to Ghana using the information in thetable, as well as your own good judgement and analytical skills.

(a) You decide to start with a fiscal assessment. What trend do you seein government revenues and expenses?

(b) You notice that neither the primary deficit nor interest expensesare reported separately. How would you estimate them from thenumbers in the table? What are their values for 2011?

(c) Using what you know about government debt dynamics, computethe ratio of government debt to GDP for 2011. What factors con-tribute the most to the change from 2010?


(d) Overall, how would you assess the risks to Ghana’s economy overthe next couple of years?

2008 2009 2010 2011 2012

GDP growth (%) 8.4 4.0 7.7 13.6 7.4Inflation (%) 18.1 16.0 8.6 8.6 8.5Interest rate (%) 20.8 28.8 22.7 20.5 20.6Govt revenue (% of GDP) 16.0 16.5 19.1 23.4 22.2Govt spending (% of GDP) 24.5 22.3 25.5 27.6 27.7Govt budget balance (% of GDP) –8.5 –5.8 –6.5 –4.2 –5.5Govt debt (% of GDP) 30.6 33.3 33.9Real exchange rate (index) 81.7 76.3 81.8 78.1 74.5FX reserves (USD billions) 1.8 2.9 4.3 4.4 4.8

Data from EIU CountryData. The government budget balance is a sur-plus if positive, deficit if negative. The real exchange rate is the price ofgoods in Ghana relative to the rest of the world; the larger the number,the more expensive goods are in Ghana. The numbers for 2011 and 2012are estimates.

Answer.

(a) Trends include: (i) revenues and spending both rising, (ii) spendingstill ahead of revenue (there’s a deficit), and (as a direct result)(iii) ratio of debt to GDP rising a little (more on that to come).

(b) This is a tricky one. Remember that interest payments in year t areitBt−1/Yt. We get what we want from:

itBt−1/Yt = it(Bt−1/Yt−1)(Yt−1/Yt)

≈ it(Bt−1/Yt−1)/(1 + gt + πt).

That gives us interest payments in 2011 of 5.7% of GDP and aprimary deficit of −1.5% (that is, a surplus).

(c) The key relation is this one:

∆(Bt/Yt) = (it − πt)(Bt−1/Yt−1)− gt(Bt−1/Yt−1) + (Dt/Yt).

We refer to the components on the right as A, B, and C. Doing thecalculations gives us

2010 2011

Interest payments 4.0Component A (interest) 4.0Component B (growth) –4.6Component C (primary deficit) –1.5Total change in B/Y –2.1Public debt (% of GDP) 33.9 31.8


Over this period, the ratio of debt to GDP fell by 2.1%. The com-ponents contributed: interest +4.0, growth –4.6, and the primarydeficit –1.5. Note especially the growth term, the result of unusuallyhigh GDP growth in 2011.

(d) This is a call to look at the checklist of crisis indicators:

• Government debt and deficits. We have deficits, but there’s notmuch sign yet of a growth debt to GDP ratio. One future con-cern might be the possibility of borrowing now against future oilrevenue. Will any debts incurred be spent wisely? Will the oilrevenue show up?

• Banking system. No information provided.

• Exchange rate and reserves. Reserves are modest, but with the ex-change rate floating there shouldn’t be much concern about that.

• Politics. Always an issue, especially with a contentious electioncoming and the promise of money from oil revenue. It’s an oddfact but a true one that revenue from natural resources is morelikely to cause problems than solve them.

Update: In August 2014, Ghana asked the IMF for help. The chance ofdefault remains low, since foreign debt is backed by oil revenue, but thepromise of oil has turned into a curse, as it often does.

2. Don’t Cry for Me Argentina. (We know, it’s a cliche, but so is theirapproach to policy.) Argentina is a seemingly endless source of entertain-ment to economists, yet its economy has done well in the recent past.GDP growth fell to 0.9% in 2009, during the global financial crisis, butaveraged over 9% the next two years. Most analysts attribute this successto favorable commodity prices and strong global demand for Argentina’scommodity exports. Additional information is provided in Table 21.1.

At the same time, the government of President Cristina Fernandez deKirchner continues to adopt policies that befuddle outside observers, in-cluding: taking over private pension funds, restricting imports and pur-chases of foreign currency, attacking the press, nationalizing the Spanish-owned oil company YPF, imposing price controls on electricity, naturalgas, and public transportation, and subsidizing energy consumption.

The Economist Intelligence Unit reports:

• A US court case may eventually leave Argentina with the unpalatablechoice of repaying the “holdouts” (creditors that did not participate inthe 2005 or 2010 restructurings) in full — something that it has swornnever to do — or falling into default with its remaining creditors.

• According to official data, consumer price inflation remains among thehighest in emerging markets, at 10.5% in April 2013. However, theofficial data are widely discredited and we are now using estimates


2010 2011 2012 2013

Official exchange rate (pesos per USD) 3.90 4.11 4.54 5.46Inflation (%) 22.9 24.4 25.3 20.6Foreign currency reserves (USD billions) 52.2 46.4 43.2 32.2Real GDP growth (%) 9.2 8.9 1.9 5.2Govt revenue (% of GDP) 24.3 23.6 25.4 27.3Govt spending (% of GDP) 24.1 25.3 28.0 30.5Public sector surplus (% of GDP) 0.2 –1.7 –2.6 –3.2Primary balance (% of GDP) 1.7 0.3 –0.2 –0.8Govt debt (yearend, % of GDP) 44.8Interest rate paid on debt (%) 4.0 5.5 6.7 6.5Money market interest rate (%) 9.1 10.0 9.8 12.7

Table 21.1: Economic indicators for Argentina. Source: EIU.

produced by PriceStats, which estimates that inflation in 2012 was25%.

• Double-digit inflation has generated real peso appreciation. Foreign-exchange controls have failed to prevent an erosion of foreign exchangereserves, heightening the risk of an eventual devaluation.

• The Argentine peso floats in principle, but the central bank intervenesto limit its rate of depreciation. In addition, foreign currency transac-tions are subject to a variety of controls. For the past couple of years,the government has been gradually tightening the “clamp,” an unoffi-cial policy of discouraging purchases of dollars. As a result, the peso’sofficial decline has been modest, but the unofficial “blue market” priceof the peso is considerably lower.

• The poor banking sector risk rating reflects weak economic activity,expansionary monetary policies that contribute to credit risk, high riskof exchange-rate and interest-rate volatility, and increased currencyconvertibility risk.

• The ruling party fared badly in the October midterm election, leavingthe president without enough support in Congress to change the consti-tution and run for re-election. Focus will now shift rapidly to the 2015presidential race. The president remains alienated from almost all ofthe country’s most influential groups, including the unions, the media,the Catholic Church and the traditional leaders of the Peronist party.In this context, risks to political stability will be high. An additionalrisk to stability is the president’s health.

The question is what happens next: Could another crisis be on the way,or has Argentina put its problematic past to rest? Use the information


provided, including Table 21.1, to assess the risks to the Argentina econ-omy over the next 2-3 years.

(a) By “real appreciation” we mean an increase in the price of localgoods relative to foreign goods — what is sometimes called a de-cline in the real exchange rate. Use the numbers in the table todemonstrate (or disprove) real appreciation of the peso.

(b) Why do you think the central bank’s foreign exchange reserves havedeclined?

(c) How do you see government debt evolving? Compute, in particular,the ratio of government debt to GDP at year-end 2013. What factorscontribute the most to the change in the ratio?

(d) Overall, how would you rate the risk of a macroeconomic crisis inArgentina? What are the biggest sources of concern?

Answer.

(a) The issue is the real exchange rate RER = eP ∗/P , where e is theexchange rate (the peso price of one dollar), P is the price of Argen-tine goods, and P ∗ is the price of American goods. So how is thereal exchange rate changing? In words: the combination of high in-flation and more modest currency depreciation has made Argentinegoods expensive (equivalently, foreign goods cheap).

How would you show this? Inflation is the rate of increase in P , andwe see the price of Argentine goods going up rapidly, roughly 20%a year. In contrast, eP ∗ is going up less: P ∗ is roughly flat (1-2%inflation in the US) and e is rising (if we compute its rate of change)5% in 2011 and 10% in 2012. Thus RER is rising, as Argentinegoods get relatively more expensive.

(b) Evidently people want dollars, not pesos, and the central bank sup-plies them to maintain a relatively stable exchange rate. One possi-ble reason: Argentine prices are rising, and a substantial deprecia-tion is one way to get that. That makes pesos less attractive, sinceyou’d lose (relative to dollars) if the peso falls in value.

(c) The debt dynamics equation is

∆(Bt/Yt) = (it − πt)(Bt−1/Yt−1)− gt(Bt−1/Yt−1) +Dt/Yt.

The three terms are

(it − πt)(Bt−1/Yt−1) = −6.3

−gt(Bt−1/Yt−1) = −2.3

Dt/Yt = 0.8.

Their total is –7.8, so the ratio of debt to GDP will fall to 37.0. Notefor later the negative contribution of the real interest rate: they’re


getting a very good deal on their debt. It’s not hard to imagine thatchanging.

(d) This is a call for the checklist:

• Debt and deficits. (i) The calculation shows the debt ratio isfalling. But the US court case could lead to default, which isn’t agood thing. And the negative real interest rate is unlikely to con-tinue. If they paid a modest 2% real rate on debt, the debt ratiowould go up about 4% this year, and higher rates are certainlypossible.

• Banks. The EIU suggests that banks could suffer from a weakeconomy.

• Exchange rates and reserves. The real exchange rate continuesto appreciate, making Argentine goods more expensive. At thesame time, they’re losing reserves as they sell dollars to supportthe peso. Both point toward a decline in the value of the peso.

• Politics. Always an issue in Argentina. There’s some uncertaintygiven the president’s lame duck status and health. On the otherhand, a change could make things better.

The fiscal situation, including the court case, the exchange rate andreserve position, the banking system, and the political situation allshows signs of trouble. Overall, they’ll probably muddle through,but there’s a chance of serious trouble.

Update: Argentina defaulted in July 2014. It’s not clear how this willplay out, but “muddle through” seems to be the likely outcome. Thishasn’t had a large impact to date because Argentina was already lockedout of international financial markets for new issues. The default doesn’tchange that, although it does make some international transactions moredifficult.


You can find similar analyses in many places. One of our favorites is theEconomist Intelligence Unit’s Country Risk Reports. Another is the IMF’sVulnerability Indicators.

There’s no end of good descriptions of crises. On the most recent crisis, BenBernanke’s testimony to the crisis commission is a good overview from theperspective of the US (search: “Bernanke testimony crisis causes”). MichaelLewis’s Vanity Fair pieces are works of art (search “michael lewis vanityfair”). Among the many books about crises, we recommend

• Robert Bruner and Sean Carr, The Panic of 1907 . Good read, and short;you’ll think it’s about 2007.

http://www.imf.org/external/np/exr/facts/vul.htm

http://www.federalreserve.gov/newsevents/testimony/Bernanke20100902a.htm

http://www.amazon.com/Panic-1907-Lessons-Learned-Markets/dp/0470452587/


• Carmen Reinhart and Kenneth Rogoff, This Time is Different . The recentbestseller, covering 800 years and the whole world.

• David Wessel, In Fed We Trust . Terrific book from the Wall Street Jour-nal writer.

• Paul Blustein, And the Money Kept Rollin In (and Out). Wonderful re-view of Argentina’s 1999-2001 crisis. He has another one, The Chastening ,about the Asian crisis and the IMF.

http://www.amazon.com/This-Time-Different-Centuries-ebook/dp/B004EYT932/

http://www.amazon.com/Fed-We-Trust-Bernankes-Great/dp/0307459683/

http://www.amazon.com/dp/1586483811/


Index

absolute advantage, 110accession rate, 94, 97adult population, 88, 99aggregate demand (AD), 164, 166–

169, 176, 177aggregate supply (AS), 160, 164–

169, 176–180, 182long-run aggregate supply, 165,

167, 176, 177, 180, 182short-run aggregate supply,

165, 169, 172annual compounding, 6, 11AS/AD model, 175, 194ask price, 91autarky, 111average product of labor, see labor

basis point, 187Bernanke, Ben, 36, 86, 108, 192, 198,

272bond, 4, 11, 105, 155, 156, 158, 159,

186–189, 192, 193, 195,232–235, 252, 257, 258

bond duration, 11bond yield, 3, 4, 4, 11, 132, 133,

141, 158, 160, 186, 187,194, 195, 197

budget deficit, seegovernment budget

business cycle, 128–133, 169, 171,193

countercyclical, 136, 136, 140,143

procyclical, 132, 136, 140–142scorecard, 142, 143, 146

capital, 46, 48

human capital, 49, 50, 54, 74–76

marginal product of, 3, 11, 12,46, 47, 51–53, 55, 195

market return on, 53

physical capital, 23, 46, 49, 53,164

capital controls, seeexchange rate regimes

central bank, 80, 82, 106, 155–157,160, 171, 180, 181, 187–193, 195–197, 204, 227,232, 243, 247, 256–259,261, 266, 267

chain weighting, 30

Cobb-Douglas, seeproduction function

coincident indicator, seecyclical indicators

comparative advantage, 110, 111, 114

competitive markets, 52, 81

consumer price index (CPI), seeprice index

consumer surplus, 207, 208, 213

consumption possibility frontier, 111

convergence, see Solow model

convertibility, seeexchange rate regime

corporate governance, 106

countercyclical, see business cycle

covered interest parity, seeinterest rate parity

credit easing, see monetary policy

credit risk, 187

default risk, 106, 219, 227

creditor protection, 106

275


crisiscrisis indicators, 264crisis responses, 266

cross-correlation function, 138–142current account, 30, 232, 233, 235–

238cyclical indicators, 129, 143

coincident indicator, 136lagging indicator, 136leading indicator, 136

debt, see government debtdefault risk, see credit riskdeflation, 26, 196deflator, see price indexdemand function, 4deposit insurance, 107depreciation, see exchange ratederivative (calculus), 10disclosure, 106

equilibrium, 114, 167excess burden, see taxexchange rate, 242

appreciation, 242conventions, 242depreciation, 242, 246devaluation, 242real, 242revaluation, 242sterilized intervention, 258

exchange rate regime, 255capital controls, 204, 256convertibility, 255fixed exchange rate, 187, 242,

256, 259–261, 263, 266flexible exchange rate, 256floating exchange rate, 256managed float, 256pegged exchange rate, 256speculative attacks, 259trilemma of open-economy mon-

etary policy, 258expected inflation, see inflationexpenditure identity of GDP, see

identitiesexternality, 118

financial markets, 105

financial regulation, 106fiscal discipline, 225fiscal dominance, 152fiscal policy, 220fixed exchange rate, see

exchange rate regimefixed-basket approach, see

price indexfixed-weight approach, see

price indexflexible exchange rate, see

exchange rate regimefloating exchange rate, see

exchange rate regimeforecasting, 136FRED database, 15Friedman, Milton, 107, 152function, 3

GDP, see gross domestic productGDP deflator, see price indexgovernance, 80government budget, 219–227

budget constraint, 155, 156,220, 221

budget (or government) deficit,25, 26, 82, 152, 156, 157,213, 220, 221, 219–227

primary deficit, 220–227government debt, 220–227

debt-to-GDP ratio, 220, 222off-balance-sheet liabilities, 226sovereign debt, 263sustainability, 236unsustainable, 237

government deficit, seegovernment budget

government purchases, see gross do-mestic product (GDP)

government saving, see savingGreat Moderation, 128gross domestic product (GDP)

government purchases, 24investment, 23net exports, 24nominal GDP, 26, 222, 223payments to labor and capital,

20

INDEX 277

per capita GDP, 74real GDP, 7–10, 15, 26–29, 30–

32, 46, 48, 52, 70, 73, 127–129, 131, 136, 152, 153,189, 223, 224

value added, 20, 21value of final goods, 20, 21

gross national product (GNP), 29growth accounting, 70–73, 76, 78growth rate, 6

continuously compounded, 8, 9,16, 72

discretely compounded, 6–8

Henry, Peter, 81hidden liabilities, 226

financial bailouts, 226off-balance-sheet liabilities, 226regional governments, 226social security and pensions, 226

identities, 22expenditure identity of GDP, 23flow-of-funds identities, 25income identity of GDP, 22

income identity of GDP, seeidentities

industrial production, 136–137, 139–146

industrial production (IP), 140inflation, 26–29, 80, 82, 135, 151–

154, 156–160, 171, 175,176, 178–180, 186, 189,191–195, 197, 198, 214, 267

expected inflation, 157hyperinflation, 152

inflation target, see monetary policyinflation targeting, see

monetary policyinstitutions, 79, 98, 227interest rate, 157–161, 166, 167,

185–197, 211, 220–226,248–252, 260

long-term, 187, 191nominal, 156–161, 186, 188–190,

194, 196, 221real, 158, 186, 194, 195, 211,

223, 224

term structure of interest rates,186

interest rate parity, 243, 248covered interest parity, 248uncovered interest parity, 249

interest-rate rules, seemonetary policy

intervention, 258investment, see gross

domestic product (GDP)

job creation rate, see laborjob destruction rate, see laborjob reallocation rate, see laborjob turnover rate, see labor

Keynes, John Maynard, 164Kydland, Fynn, 80

labor, 49average product of labor, 51demand for labor, 89inactive population, 88job creation rate, 94job destruction rate, 94job reallocation rate, 94job turnover rate, 94labor force, 63, 88labor market equilibrium, 91labor market flows, 93labor market institutions, 93marginal product of, 90participation rate, 88steady-state unemployment

rate, 96unemployment dynamics, 96unemployment rate, 88worker reallocation rate, 94

labor market, see laborlabor market equilibrium, see laborlagging indicator, see

cyclical indicatorslaw of one price, 244leading indicator, see

cyclical indicatorslevel accounting, 70, 71, 76logarithm, 5long-run aggregate supply, see


aggregate supplylong-term interest rate, see

interest rate

managed float, seeexchange rate regime

marginal cost, 10, 90marginal product

marginal product of capital, 16marginal product of labor, 90

minimum wage, 91monetary policy, 152, 187

credit easing, 196forward guidance, 197goals, 191inflation target, 193inflation targeting, 193interest-rate rules, 193money supply, 154open-market operation, 187, 189policy discretion, 259policy duration commitment,

197quantitative easing, 196–198rules vs discretion, 193sterilization, 258Taylor rule, 193zero lower bound, 196

money supply, see monetary policymoral hazard, 107

net exports, seegross domestic product

(GDP)nominal GDP, see

gross domestic productnominal interest rate, see

interest rate

off-balance-sheet liabilities, seehidden liabilities

open-market operation, seemonetary policy

output gap, 176, 194

partial derivative, 12, see derivativeparticipation rate, see laborpegged exchange rate, see

exchange rate regimeper capita GDP, see

gross domestic productphysical capital, see capitalpolicy discretion, see monetary pol-

icypolicy duration commitment, see

monetary policyPonzi scheme, 222population, 88potential output, 176PPP, see purchasing power parityPrescott, Edward, 80presidential futures markets, 147price index, 26, 151

consumer price index (CPI), 15,27, 28, 147, 161, 245

deflator, 26, 30fixed-basket approach, 27fixed-weight approach, 27, 28GDP deflator, 26

price level, 26primary deficit, see

government budgetprivate saving, see savingprocyclical, see business cycleproducer surplus, 207production function, 4, 45, 69

Cobb-Douglas, 47production possibility frontier, 111productivity, 51

labor productivity, 116total factor productivity (TFP),

51–53, 55, 70–73, 75, 76,117

property rights, 80public debt, see government debtpurchasing power parity (PPP), 31,

243

quantitative easing, seemonetary policy

quantity theory of money, 152–154

real GDP, see gross domestic prod-uct (GDP)

real interest rate, see interest raterecession, 129

INDEX 279

returns to scale, constant, 46Ricardo, David, 110risk premium, 187rule of law, 80rules vs discretion, see

monetary policy

Sargent, Thomas, 156saving, 25, 63

government saving, 25gross domestic saving, 25private saving, 25

seasonal adjustment, 31separation rate, 94short-run aggregate supply, see ag-

gregate supplyshort-term interest rate, see

interest rateSolow model, 58–63

convergence, 60Solow, Robert, 58sovereign debt, see government debtspeculative attack, see

exchange rate regimespeed of adjustment, 98, 102spreadsheet, 13steady-state unemployment rate, see

laborsticky prices, 165sticky wages, 164, 168supply of labor, see laborsupply shocks, 169, 177, 195sustainability, see government debt

tax, 205broad tax-base principle, 208capital income tax, 211deadweight loss, 208excess burden, 208social cost, 207tax base, 206, 208

tax rate, 212tax wedge, 206value-added tax (VAT), 210welfare loss, 208

Taylor rule, see monetary policyTaylor, John, 193term structure of interest rates, see

interest ratetime consistency, 80, 107, 157, 191,

193, 212, 219, 227, 259, 260too big to fail, 107total factor productivity, see

productivitytrade, 110

trade balance, 24trade politics, 119

Treasury, 187balance sheet, 187Treasury bill, 158

Treasury bill, see Treasurytrilemma of open-economy monetary

policy, see exchange-rateregime

uncovered interest parity, seeinterest rate parity

underground economy, 29, 209unemployment dynamics, see laborunemployment rate, see laborunsustainable, see government debt

value-added tax (VAT), see taxvelocity of money, 153, 159volatility of output, 128

welfare loss, see taxworker reallocation rate, see labor

yield, see bond

zero lower bound, seemonetary policy

Documents

The Global Economy - NYU Stern